Math Olympiad | A Nice Algebra Problem | Find the values of X

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  • เผยแพร่เมื่อ 24 ธ.ค. 2024

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  • @is7728
    @is7728 5 หลายเดือนก่อน +13

    Let h be x + 1.
    (h + 1)^4 + h^4 = 17
    h^4 + 4h^3 + 6h^2 + 4h + 1 + h^4 = 17
    2h^4 + 4h^3 + 6h^2 + 4h - 16 = 0
    h^4 + 2h^3 + 3h^2 + 2h - 8 = 0
    When h = 1, the eqn is satisfied.
    ∴ x = 0
    h^3 + 3h^2 + 6h + 8 = 0
    When h = -2, the eqn is satisfied.
    ∴ x = -3
    h^2 + h + 4 = 0
    h = ( -1 +- √(1 - 16) ) / 2
    = -0.5 +- √15 i / 2
    ∴ x = -1.5 +- √15 i / 2

  • @xyz9250
    @xyz9250 3 หลายเดือนก่อน +1

    If had to go through expansion why not just expand the original equation and solve it directly? But here is how I did it. (x+2)^4 - 1 + (x+1)^4 - 4^2 =0 …. Will get x = -3 and 0 pretty quickly, then use the formula to get the two solutions of complex numbers

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      *complex numbers

    • @xyz9250
      @xyz9250 3 หลายเดือนก่อน

      You are correct. Edited

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน +1

      That's a nice way to factor the quartic equation!
      (x+2)⁴ + (x+1)⁴ = 17 = 2⁴ + 1⁴
      (x+2)⁴-1⁴ + (x+1)⁴-2⁴ = 0
      ((x+2)²-1²)*((x+2)²+1²) + ((x+1)²-2²)*((x+1)²+2²) = 0
      (x+1)*(x+3)*(x²+4*x+5) + (x-1)*(x+3)*(x²+2*x+5) = 0
      (x+3)*[(x+1)*(x²+4*x+5) + (x-1)*(x²+2*x+5)] = 0
      (x+3)*[ x*Σ + 1*∆ ] = 0
      (x+3)*[ x*(2*x²+6*x+10) + 1*(2*x) ] = 0
      (x+3)*[ 2*x*(x²+3*x+5 + 1) ] = 0
      2*x*(x+3)*(x²+3*x+6) = 0
      x = 0, -3, (-3 ± i*√15)/2
      Most folks would the sum of differences of 4th powers by pairing like terms: (x+2)⁴-2⁴ + (x+1)⁴-1⁴ = 0 . And the next step will reveal x can be factored out easily. But that leaves a cubic polynomial -- it may be hard to find x+3 as a factor to reduce that down. By pairing the counterintuitive way [(x+2)⁴-1⁴ + (x+1)⁴-2⁴ = 0], factor x+3 is removed first, leaving the cubic polynomial that's easily reduced by factoring out x. This is useful when someone creates a challenge with the sum of the 4th power of consecutive integers: 0⁴+1⁴=1, 1⁴+2⁴=17, 2⁴+3⁴=97, 3⁴+4⁴=337, 881, 1921, 3697, 6497, 10657, 16561, ...

  • @henkn2
    @henkn2 5 หลายเดือนก่อน +2

    It might be helpful not to the use the same letters (a, b and c) with different meanings (first a = x + 2 and b = x + 1, later they are used in the equation ax^2 + bx + c = 0). Furthermore the non-real (complex) solutions have been skipped

  • @jenskluge7188
    @jenskluge7188 4 หลายเดือนก่อน

    since x=0 is a solution we can already factor that out, and for polynomes of degree 3 there are formulas. if there is another obvious solution the problem can be further simplied to a 2nd degree polynomial.

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      Yes, there's another obvious solution. The exponent is 4, an even number, so ± bases yield the same value.
      (2)⁴ + (1)⁴ = 17 , for x = 0
      (-2)⁴ + (-1)⁴ = 17
      But the terms must be swapped to match the equation:
      (-1)⁴ + (-2)⁴ = 17 , for x = -3
      Thus, x and x+3 are factors of the quartic equation. The missing factor is a quadratic polynomial that yields a complex conjugate pair of roots, (-3 ± i*√15)/2 .

  • @maximcoroli8306
    @maximcoroli8306 5 หลายเดือนก่อน +1

    17 = 1**4 +2**4 or (-1)**4+(-2)**4
    х+2=2, х+1=1 => x=0
    x+2=-1, x+1=-2 = x=-3

  • @ashkanshekarchi7753
    @ashkanshekarchi7753 5 หลายเดือนก่อน +11

    Explain the solving strategy and ideas rather than a long confusing mechanical calculation

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      His obfuscated way is unnecessarily complicated. It's faster to do the binomial expansion and solve:
      (x⁴ + 4*2*x³ + 6*2²*x² + 4*2³*x + 2⁴) +
      (x⁴ + 4*x³ + 6*x² + 4*x + 1) = 17
      2*x⁴ + 12*x³ + 30*x² + 36*x + 17 = 17
      x⁴ + 6*x³ + 15*x² + 18*x = 0 ‡
      x*((x + 3)*x² + (x + 3)*3*x + (x + 3)*6) = 0
      x*(x + 3)*(x² + 3*x + 6) = 0
      x = 0, -3, (-3 ± i*√15)/2
      { ‡ In the original equation, the values in parentheses work for 2⁴+1⁴ and (-1)⁴+(-2)⁴ . Thus, we know x = 0 and -3 . We know x and x+3 are factors. }
      In general, a² - b² isn't a perfect square.
      ∆ is called the "discriminant".
      At 07:20, he can complete the square:
      z² + 2*z + 1 = 9 , z = a*b
      z + 1 = ±3
      z = -1 ± 3 = 2, -4
      There's no reason to reject the complex solutions.

  • @oahuhawaii2141
    @oahuhawaii2141 3 หลายเดือนก่อน

    It's faster to do the binomial expansion and solve.
    Your obfuscated way is unnecessarily complicated.
    In general, a² - b² isn't a perfect square.
    ∆ is called the "discriminant".
    At 07:20, you can complete the square:
    Z² + 2*Z + 1 = 9 , Z = a*b
    Z + 1 = ±3
    Z = -1 ± 3 = 2, -4
    There's no reason to reject the complex solutions.

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      (x⁴ + 4*2*x³ + 6*2²*x² + 4*2³*x + 2⁴) +
      (x⁴ + 4*x³ + 6*x² + 4*x + 1) = 17
      2*x⁴ + 12*x³ + 30*x² + 36*x + 17 = 17
      x⁴ + 6*x³ + 15*x² + 18*x = 0
      x*(x³ + 6*x² + 15*x + 18) = 0
      x*((x + 3)*x² + (x + 3)*3*x + (x + 3)*6) = 0
      x*(x + 3)*(x² + 3*x + 6) = 0
      x = 0, -3, (-3 ± i*√15)/2

  • @nasrullahhusnan2289
    @nasrullahhusnan2289 5 หลายเดือนก่อน

    Note the special contion here. As 2⁴+1⁴=17 and the power is even then the sign of 2 can be + or -. Similarly the sign og 1. Both can be the same sign, or not. And x is found accordingly.

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      His obfuscated way is unnecessarily complicated. It's faster to do the binomial expansion and solve. It turns out that no substitution is faster and less error-prone.
      (x⁴ + 4*2*x³ + 6*2²*x² + 4*2³*x + 2⁴) +
      (x⁴ + 4*x³ + 6*x² + 4*x + 1) = 17
      2*x⁴ + 12*x³ + 30*x² + 36*x + 17 = 17
      x⁴ + 6*x³ + 15*x² + 18*x = 0 ‡
      x*((x + 3)*x² + (x + 3)*3*x + (x + 3)*6) = 0
      x*(x + 3)*(x² + 3*x + 6) = 0
      x = 0, -3, (-3 ± i*√15)/2
      { ‡ Upon inspection of the original equation, the values in parentheses work for (2)⁴+(1)⁴ and (-1)⁴+(-2)⁴ . Thus, we know x = 0 and x = -3 , and that x and x+3 are factors of the quartic equation. Factor them out to leave a quadratic equation for the complex conjugate pair of roots, x = (-3 ± i*√15)/2 . }

  • @joiceroosita5317
    @joiceroosita5317 5 หลายเดือนก่อน +1

    Mine is more simple.
    (x+2)⁴ + (x+1)⁴ = 17
    [(x+1)+1]⁴ + (x+1)⁴ = 17
    example ; y = (x+1)
    (y+1)⁴ + y⁴ = 17
    y⁴ + 4y³ + 6y² + 4y + 1 + y⁴ - 17 = 0
    2y⁴ + 4y³ + 6y² + 4y - 16 = 0
    2(y⁴ + 2y³ + 3y² +2y - 8) = 0
    Lets find the factors of y
    Using polinomial
    Factors of y⁴ + 2y³ + 3y² + 2y - 8 = 0
    (y - 1) → y = 1 → 1+2+3+2-8 = 0 (ok!)
    (y + 2) → y = -2 → -8+12-12+8 = 0 (ok.!)
    The others y = i
    So, we get y = 1 and y = -2
    (y = x+1)
    y = 1
    x+1 = 1 → x = 0 (check ok.!)
    y = -2
    x+1 = -2 → x = -3 (check ok.!)
    So, x = 0, -3

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      Factor out x and x+3 to leave a quadratic equation. You can easily get the complex conjugate pair of roots, (-3 ± i*√15)/2 .

  • @AlexMarkin-w6c
    @AlexMarkin-w6c 4 หลายเดือนก่อน

    Let y=x+1.5, then (y+0.5)^4+(y-0.5)^4=17 (4y^2-9)(4y^2+15)=0; y=+/-3/2 and y= +/-isqrt(15)/2. If y=x+1.5, then x=-3, x=0, , x=-1.5 +/- isqrt(15)/2

  • @thomassidoti5496
    @thomassidoti5496 5 หลายเดือนก่อน +2

    Its a 4th degree equation. Theres 4 solutions. You missed the two complex solutions; x= (-3/2) +or- (radical(15)i/2). This is an OLYMPIAD question. Those solutions belong there

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      x = 0, -3, (-3 ± i*√15)/2

  • @СалохиддинФазлиддинов-е5м
    @СалохиддинФазлиддинов-е5м 5 หลายเดือนก่อน +27

    Is here anybody, who automatically calculated that x=0😂😂
    Being honest, I didn't watch till the end, because I already thought that 2^4+1^4 equals to 17
    And second x equals to -3

    • @laoxian899
      @laoxian899 5 หลายเดือนก่อน +3

      Yes, at the first glance one can get the two results, since both parentheses must be 1/-1 and 2/-2.

    • @abbasmasum1633
      @abbasmasum1633 5 หลายเดือนก่อน +1

      The goal is to learn how to apply several rules of algebra to find the solutions. This channel is the best there is and PLEASE stop offering guess and check solutions. He's connecting the problem to so many profound concepts. I truly like his methods and if they are too long, then at least offer a better way.

    • @professorsargeanthikesclim9293
      @professorsargeanthikesclim9293 5 หลายเดือนก่อน

      Did you also find the complex solutions?

    • @robertloveless4938
      @robertloveless4938 5 หลายเดือนก่อน

      I did. Had the number NOT been -1, 0, or +1, I would have worked it out. But a quick inspection worked this time.

    • @heikelawin3771
      @heikelawin3771 4 หลายเดือนก่อน

      Natürlich!
      Diese Lösung springt einem ja mit 'nem nackten Ar... ins Auge!!!!

  • @opulence3222
    @opulence3222 5 หลายเดือนก่อน +11

    Very confusing procedure.

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      He's going for obfuscation. The direct solution is faster, and less prone to mistakes.

  • @thomaslangbein297
    @thomaslangbein297 5 หลายเดือนก่อน +1

    What did we learn?

  • @is7728
    @is7728 5 หลายเดือนก่อน +2

    2^4 + 1^4 = 17
    (-1)^4 + (-2)^4 = 17

  • @walterwen2975
    @walterwen2975 5 หลายเดือนก่อน

    Math Olympiad: (x + 2)⁴ + (x + 1)⁴ = 17; x = ?
    Second method;
    Let: y = x + 3/2, a = 1/2; (x + 2)⁴ + (x + 1)⁴ = (y + a)⁴ + (y - a)⁴ = 17
    (y ± a)⁴ = y⁴ ± 4ay³ + 6a²y² ± 4a³y + a⁴, (y + a)⁴ + (y - a)⁴ = 2y⁴ + 12a²y² + 2a⁴ = 17
    2y⁴ + 12(1/4)y² + 2(1/16) = 17, 2y⁴ + 3y² + 1/8 = 17, 16y⁴ + 24y² + 1 = 136
    16y⁴ + 24y² - 135 = 0, (2y)⁴ + 6(2y)² - 135 = [(2y)² - 9][(2y)² + 15] = 0
    (2y)² - 9 = 0, (2y)² = 9; 2y = ± 3 or (2y)² + 15 = 0, 2y = ± i√15; y = x + 3/2
    2y = 2(x + 3/2) = 2x + 3 = ± 3; x = 0 or x = - 3
    2y = 2(x + 3/2) = 2x + 3 = ± i√15; x = (- 3 ± i√15)/2

  • @santer70
    @santer70 4 หลายเดือนก่อน

    And about the unreal solutions ?

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      Too complex for him perhaps?

  • @salamoujda3651
    @salamoujda3651 4 หลายเดือนก่อน

    thanks bravo!

  • @丁爸爸-w3f
    @丁爸爸-w3f 5 หลายเดือนก่อน

    一秒钟做出来,0和-3.还有其他解么?

    • @lthakur92411
      @lthakur92411 4 หลายเดือนก่อน

      no

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      x = 0, -3, (-3 ± i*√15)/2

  • @walterwen2975
    @walterwen2975 5 หลายเดือนก่อน +2

    Math Olympiad: (x + 2)⁴ + (x + 1)⁴ = 17; x = ?
    Let: y = x + 2; y⁴ + (y - 1)⁴ = 2y⁴ - 4y³ + 6y² - 4y + 1 = 17
    2y⁴ - 4y³ + 6y² - 4y = 16, y⁴ - 2y³ + 3y² - 2y - 8 = 0
    (y⁴ - 2y³ + y²) + (2y² - 2y) - 8 = 0, (y² - y)² + 2(y² - y) - 8 = 0
    (y² - y - 2)(y² - y + 4) = (y + 1)(y - 2)(y² - y + 4) = 0
    y + 1 = 0, y = - 1; y - 2 = 0, y = 2 or y² - y + 4 = 0, y = (1 ± i√15)/2
    x = y - 2: x = - 3; x = 0 or x = (1 ± i√15)/2 - 2 = (- 3 ± i√15)/2
    Answer check:
    x = - 3: (x + 2)⁴ + (x + 1)⁴ = (- 1)⁴ + (- 2)⁴ = 1 + 16 = 17; Confirmed
    x = 0: 2⁴ + 1⁴ = 16 + 1 = 17; Confirmed
    x = (- 3 ± i√15)/2: y = x + 2, y² - y + 4 = 0, y² - y = - 4
    (x + 2)⁴ + (x + 1)⁴ = 2(y⁴ - 2y³ + 3y² - 2y) + 1 = 2[(y² - y)² + 2(y² - y)] + 1
    = 2[(- 4)² + 2(- 4)] + 1 = 2(16 - 8) + 1 = 17; Confirmed
    Final answer:
    x = - 3, x = 0, Two complex value roots, if acceptable;
    x = (- 3 + i√15)/2 or x = (- 3 - i√15)/2

    • @NNaween
      @NNaween 5 หลายเดือนก่อน

      Nice explanation
      @naweenraaj

    • @is7728
      @is7728 5 หลายเดือนก่อน

      Maybe this better?
      Let h be x + 1.
      (h + 1)^4 + h^4 = 17
      h^4 + 4h^3 + 6h^2 + 4h + 1 + h^4 = 17
      2h^4 + 4h^3 + 6h^2 + 4h - 16 = 0
      h^4 + 2h^3 + 3h^2 + 2h - 8 = 0
      When h = 1, the eqn is satisfied.
      ∴ x = 0
      h^3 + 3h^2 + 6h + 8 = 0
      When h = -2, the eqn is satisfied.
      ∴ x = -3
      h^2 + h + 4 = 0
      h = ( -1 +- √(1 - 16) ) / 2
      = -0.5 +- √15 i / 2
      ∴ x = -1.5 +- √15 i / 2

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน +1

      @is7728: It turns out that no substitution is faster and less error-prone. Upon inspection of the original equation, the values in parentheses work for 2⁴+1⁴ and (-1)⁴+(-2)⁴ . Thus, we know x = 0 and x = -3 . We know x and x+3 are factors of the quartic equation. Factor them out to leave a quadratic equation for the complex conjugate pair of roots, (-3 ± i*√15)/2 .
      (x⁴ + 4*2*x³ + 6*2²*x² + 4*2³*x + 2⁴) +
      (x⁴ + 4*x³ + 6*x² + 4*x + 1) = 17
      2*x⁴ + 12*x³ + 30*x² + 36*x + 17 = 17
      x⁴ + 6*x³ + 15*x² + 18*x = 0
      x*((x + 3)*x² + (x + 3)*3*x + (x + 3)*6) = 0
      x*(x + 3)*(x² + 3*x + 6) = 0
      x = 0, -3, (-3 ± i*√15)/2

    • @is7728
      @is7728 3 หลายเดือนก่อน

      @@oahuhawaii2141 But your factorization from cubic to quadratic eqns is quite subtle to notice

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      The polynomial coefficients used in synthetic division, with annotations:
      1 6 15 18 / 1 3 = 1 3 6
      1 3 { 1 3 * 1 _ _ }
      0 3 15 18
      0 3 9 { 1 3 * 0 3 _ }
      0 0 6 18
      0 0 6 18 { 1 3 * 0 0 6 }
      { 1 _ _ + 0 3 _ + 0 0 6 = 1 3 6 }

  • @E.h.a.b
    @E.h.a.b 5 หลายเดือนก่อน +2

    Let y = x + 3/2
    (y + 1/2)^4 + (y - 1/2)^4 = 17
    (y^2 + y + 1/4)^2 + (y^2 - y + 1/4)^2 = 17
    [ (y^2 + 1/4) + y ]^2 + [ (y^2 + 1/4) - y ]^2 = 17
    [ (y^2 + 1/4)^2 + 2 y (y^2 + 1/4) + y^2 ] + [ (y^2 + 1/4)^2 - 2 y (y^2 + 1/4) + y^2 ]=17
    2((y^2 + 1/4)^2 + y^2) = 17
    2(y^4 + 1/2 y^2 + 1/16 + y^2) = 17
    2 y^4 + y^2 + 1/8 + 2 y^2 - 17 = 0
    2 y^4 + 3 y^2 - 135/8 = 0
    y^2 = (-3 +/- √(9 - 4 * 2 * (- 135/8)))/(2*2)
    y^2 = (-3 +/- √(9 + 135))/4
    y^2 = (-3 +/- √144)/4
    y^2 = (-3 +/- 12)/4
    y^2 = (-3 + 12)/4 = 9/4 //y^2 = (-3 - 12)/4 < 0 so it is rejected
    y = +/- 3/2
    x = y - 3/2 = +/- 3/2 - 3/2
    x = (0, -3)

    • @Altair705
      @Altair705 5 หลายเดือนก่อน

      I made the same variable change. You could have developped faster by using the binomial expansion method:
      (a+b)^4=a⁴+4a³b+6a²b²+4ab³+b⁴
      It was even possible to skip the calculation of the terms in y and y³ by noticing that if y is solution then -y is also a solution, so only the even powers of y would remain.
      Best method in my opinion.

  • @joekfwu1
    @joekfwu1 4 หลายเดือนก่อน

    17 = 1^4 + 2^4, so (x+1)^4=2^4, (x+2)^4=1^4 then x = -3.
    what is he actually doing?

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      His obfuscated way is unnecessarily complicated. It's faster to do the binomial expansion and solve. It turns out that no substitution is faster and less error-prone:
      (x⁴ + 4*2*x³ + 6*2²*x² + 4*2³*x + 2⁴) +
      (x⁴ + 4*x³ + 6*x² + 4*x + 1) = 17
      2*x⁴ + 12*x³ + 30*x² + 36*x + 17 = 17
      x⁴ + 6*x³ + 15*x² + 18*x = 0 ‡
      x*((x + 3)*x² + (x + 3)*3*x + (x + 3)*6) = 0
      x*(x + 3)*(x² + 3*x + 6) = 0
      x = 0, -3, (-3 ± i*√15)/2
      { ‡ Upon inspection of the original equation, the values in parentheses work for (2)⁴+(1)⁴ and (-1)⁴+(-2)⁴ . Thus, we know x = 0 and x = -3 , and that x and x+3 are factors of the quartic equation. Factor them out to leave a quadratic equation for the complex conjugate pair of roots, x = (-3 ± i*√15)/2 . }

  • @davidthomas1467
    @davidthomas1467 3 หลายเดือนก่อน

    Why are you making this so bloody complicated. It's crap like this that made me fail Algebra 2 in HS. I find your videos maddening.

  • @oahuhawaii2141
    @oahuhawaii2141 3 หลายเดือนก่อน

    (x + 2)⁴ + (x + 1)⁴ = 17
    We see x = 0, -3 are 2 of 4 solutions.
    We'll use them for factoring.
    Let y = x + 1 to ease the work.
    (y + 1)⁴ + y⁴ = 17
    y⁴ + 4*y³ + 6*y² + 4*y + 1 + y⁴ = 17
    2*y⁴ + 4*y³ + 6*y² + 4*y - 16 = 0
    y⁴ + 2*y³ + 3*y² + 2*y - 8 = 0
    (y - 1)*(y³ + 3*y² - 6*y - 8) = 0
    (y - 1)*(y + 2)*(y² + y + 4) = 0
    y = 1, -2, (-1 ± i*√15)/2
    x = y - 1 = 0, -3, (-3 ± √15)/2

  • @稲次将人
    @稲次将人 4 หลายเดือนก่อน

    2^4=16だからX+2=2
    X=0
    (-2)^2=16だからX+1=-2
    X=-3
    ∴X=0,-3

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      x = 0, -3, (-3 ± i*√15)/2

    • @稲次将人
      @稲次将人 3 หลายเดือนก่อน

      I think there are no imaginary numbers in our would.

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      @稲次将人: Complex numbers are needed in STEM fields, such as physics, electronics, and math.

  • @hakanerci4372
    @hakanerci4372 3 หลายเดือนก่อน

    X=-3
    (-3+2)⁴+(-3+1)⁴=17

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      x = 0, -3, (-3 ± i*√15)/2

  • @yiutungwong315
    @yiutungwong315 5 หลายเดือนก่อน

    Real Number
    X = 0 and (-3)
    16 + 1 = 17

  • @peterlangdon6043
    @peterlangdon6043 4 หลายเดือนก่อน +1

    To be honest....videos like this tend to put students off mathematics by making it seem more complicated than it actually is....the 2 real solutions are easily derived by inspection....given the length of the video, I thought the 2 imaginary roots were going to be derived. We should be trying to teach mathematical instinct rather than complicated 'recipes'.

  • @leungwingman2061
    @leungwingman2061 4 หลายเดือนก่อน

    用二项式定理啦

  • @ramesankd1604
    @ramesankd1604 2 หลายเดือนก่อน

    പ്ളീസ്കോറെഡ് utharm

  • @Yureka-ox5jn
    @Yureka-ox5jn 4 หลายเดือนก่อน

    So cool thanks

  • @asdcuganda7572
    @asdcuganda7572 3 หลายเดือนก่อน

    Just know I got lost😂😂😂😂

  • @umranbayndr4150
    @umranbayndr4150 5 หลายเดือนก่อน

    x=0,x=-3

  • @개귀엽-f6y
    @개귀엽-f6y 2 หลายเดือนก่อน

    식을 보면 3초만에 답이 나오는데?

  • @Bertin-q3y
    @Bertin-q3y 5 หลายเดือนก่อน +1

    X=0 et.....

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      x = 0, -3, (-3 ± i*√15)/2

  • @ramesankd1604
    @ramesankd1604 2 หลายเดือนก่อน

    1

  • @CharlesChen-el4ot
    @CharlesChen-el4ot 4 หลายเดือนก่อน

    X=0; Don't do it stupidly ?!
    2 power 4 = 16
    1 power 4 = 1
    Thus 16+ 1= 17

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      Upon inspection of the original equation, the values in parentheses work for 2⁴+1⁴ and (-1)⁴+(-2)⁴ . Thus, we know x = 0 and x = -3 . We know x and x+3 are factors to the quartic equation. Factor them out to leave a quadratic equation for the complex conjugate pair of roots, (-3 ± i*√15)/2 .

  • @edwardwang7929
    @edwardwang7929 5 หลายเดือนก่อน

    Immediately guessing, x=0.

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      x = 0, -3, (-3 ± i*√15)/2

  • @Duc_Tung
    @Duc_Tung 4 หลายเดือนก่อน

    I solve it by other method.

  • @blue_white1759
    @blue_white1759 4 หลายเดือนก่อน

    Only 2 secands x=0 and -3

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน +1

      x = 0, -3, (-3 ± i*√15)/2

    • @blue_white1759
      @blue_white1759 3 หลายเดือนก่อน

      @@oahuhawaii2141 forr x€R 👍

  • @КатяРыбакова-ш2д
    @КатяРыбакова-ш2д 3 หลายเดือนก่อน

    0; -3.

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      x = 0, -3, (-3 ± i*√15)/2

  • @catchbook4268
    @catchbook4268 3 หลายเดือนก่อน

    0 / -3

  • @rgrinnell
    @rgrinnell 5 หลายเดือนก่อน

    X = 0

  • @ЛекаКузнец
    @ЛекаКузнец 4 หลายเดือนก่อน

    ОТВЕТ: Х=-3

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      Equation: (x+2)⁴ + (x+1)⁴ = 17
      ... is equivalent to: 2*x*(x+3)*(x²+3*x+6) = 0
      ... which means: x = 0, -3, (-3 ± i*√15)/2 .

  • @angelarhule4239
    @angelarhule4239 3 หลายเดือนก่อน

    I tried this 1st, got the answer in5 seconds, my god his procedure is very confusing, don’t understand a thing he’s doing, kmt 🤦‍♀️, y this long procedure?. One math problem should never take so long, very confusing, u turn off ppl from math

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      You didn't find all 4 roots in 5 seconds.

  • @makotekmachineautomationte9380
    @makotekmachineautomationte9380 3 หลายเดือนก่อน

    Ardışık 2 sayı toplamı 17. 9+8= 17 uğraşmayın bu kadar😊 şaka yapıyorum

  • @Heavenmountainway
    @Heavenmountainway 2 หลายเดือนก่อน

    Teacher passed over imaginary number. There are 4 answers

  • @박봉추-i7n
    @박봉추-i7n 5 หลายเดือนก่อน +2

    0

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      Equation: (x+2)⁴ + (x+1)⁴ = 17
      ... is equivalent to: 2*x*(x+3)*(x²+3*x+6) = 0
      ... which means: x = 0, -3, (-3 ± i*√15)/2 .

  • @angelinazheng9386
    @angelinazheng9386 4 หลายเดือนก่อน

    0。

    • @oahuhawaii2141
      @oahuhawaii2141 3 หลายเดือนก่อน

      x = 0, -3, (-3 ± i*√15)/2

  • @TWJRPGGamming
    @TWJRPGGamming 3 หลายเดือนก่อน

    0