Oxford University Software DevOps Entrance Exam

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  • เผยแพร่เมื่อ 30 ต.ค. 2024

ความคิดเห็น • 17

  • @kareolaussen819
    @kareolaussen819 5 วันที่ผ่านมา +3

    I like the way you rewrote the equation to a symmetric form❤.
    The algebra can be simplified by use of the binomial formula, with odd terms cancelling and even terms doubling.
    (t-1)^4+ (t+1)^4 = 2 (t^4 + 6 t^2 +1) = 706
    (t^2 + 3)^2 = 9 + 706/2 -1 = 361 = 19^2
    and so on...

    • @dan-florinchereches4892
      @dan-florinchereches4892 5 วันที่ผ่านมา +3

      Yes his expansion was painful. I agree with using binomial formula or deriving coefficients from Pascal's triangle

    • @9허공
      @9허공 4 วันที่ผ่านมา

      @@dan-florinchereches4892 totally agreed.

  • @PMA65537
    @PMA65537 2 วันที่ผ่านมา

    9 and 11 are both near 10.
    Rewrite perturbed eqn as
    (X + 10)^4 ~=~ 353
    Sqrt twice by rough mental arithmetic
    X + 10 ~=~ 4.2
    Test x as -6 in original eqn.

  • @barneynisbet6267
    @barneynisbet6267 4 วันที่ผ่านมา

    By inspection, 3^4=81, 5^4=625. So x=-6 and -14. Why is this difficult? Surely not any university entrance assessment? Most mathematically inclined 14 yr olds (or younger) would enjoy this problem.

    • @leealex3692
      @leealex3692 4 วันที่ผ่านมา

      Smart people states foolish, foolish people states smart.
      You state smart.

    • @fellbeast1653
      @fellbeast1653 2 วันที่ผ่านมา

      The problem is, it would be catastrophic to prove they are the ONLY solutions, better off to solve it

  • @9허공
    @9허공 4 วันที่ผ่านมา +1

    You must first say the domain of x. which is common in ALL your videos.

    • @superacademy247
      @superacademy247  4 วันที่ผ่านมา +1

      I appreciate you pointing that out! I’ll make sure to be more specific about the domain in the future. 🙏

    • @9허공
      @9허공 4 วันที่ผ่านมา

      @@superacademy247 thank you.

    • @superacademy247
      @superacademy247  วันที่ผ่านมา

      You're welcome 💕🔥🥰✅

  • @52soccerstar
    @52soccerstar 5 วันที่ผ่านมา

    Also, (x+9)^4 - 81= 625 - (x+11)^4 where 625 = 5^4 and 81 = 3^4.

  • @dwaipayandattaroy9801
    @dwaipayandattaroy9801 4 วันที่ผ่านมา

    Not liking this shit method
    put it like
    (X+ 9 ) (X+9) ( x+9) ( x+9)
    = x^2 + 18x + 81 * x^2 + 18x + 81(x+11) ^4= 706
    Muktiply both x^2+ 18x+ 81 and x^2+18x+ 81 , and show what's the product HEE HEE 💀 😂✌

    • @dwaipayandattaroy9801
      @dwaipayandattaroy9801 4 วันที่ผ่านมา

      A, b, T substitution all rubbish,NO concept there, all memory of substuting at right step, am not memorising, Explain like my way mentioned easy only concept HEE HEE 💀😂✌

  • @walterwen2975
    @walterwen2975 3 นาทีที่ผ่านมา

    Oxford University Software DevOps Entrance Exam: (x + 9)⁴ + (x + 11)⁴ = 706, x =?
    706 > (x + 11)⁴ > (x + 9)⁴ > 0 or 706 > (x + 9)⁴ > (x + 11)⁴ > 0
    Let: y = x + 10; x + 9 = y - 1, x + 11 = y + 1, (y - 1)⁴ + (y + 1)⁴ = 706
    (y ± 1)⁴ = y⁴ ± 4y³ + 6y² ± 4y + 1, (y - 1)⁴ + (y + 1)⁴ = 2(y⁴ + 6y² + 1) = 706
    y⁴ + 6y² + 1 = 353, y⁴ + 6y² - 352 = 0, (y² - 16)(y² + 22) = 0
    y² - 16 = 0; y² = 16 = 4²; y = ± 4 or y² + 22 = 0, y² = - 22; y = ± i√22
    y = x + 10 = ± 4, x = - 6; x = - 14; y = ± i√22 = x + 10, x = - 10 ± i√22
    Answer check:
    x = - 6: (x + 9)⁴ + (x + 11)⁴ = 3⁴ + 5⁴ = 706; Confirmed
    x = - 14: (- 5)⁴ + (- 3)⁴ = 5⁴ + 3⁴ = 706; Confirmed
    x = - 10 ± i√22: (± i√22 + 1)⁴ + (± i√22 - 1)⁴ = 2[(i√22)⁴ + 6(i√22)² + 1]
    = 2[(22)(22 - 6) + 1] = 2(353) = 706; Confirmed
    Final answer:
    x = - 6; x = - 14; Two complex value roots, if acceptable;
    x = - 10 + i√22 or x = - 10 - i√22