nice exponent math simplification | find the value of x

hi my family its a nice exponent math simplification if you liked thus video please like snd subscribe my channel😘

[@sharonmarshall3671]

I reduced 87/21 to 3 from the beginning which reduced the working going forward

[@amir_ismaili]

interesting 👏👏

[@Math_with_aram]

Glad you think so!

[@walterwen2975]

Nice exponent math simplification: (x⁷ + x⁵ + x³)/(x⁶ + x⁵ + x⁴) = 81/27; x = ?
(x⁷ + x⁵ + x³)/(x⁶ + x⁵ + x⁴) = [(x³)(x⁴ + x² + 1)]/[(x⁴)(x² + x + 1)] = [3(27)]/27 = 3
x ≠ 0, x ≠ ± 1; (x⁴ + x² + 1)/(x² + x + 1) = [(x⁶ - 1)/(x² - 1)]/(x² + x + 1) = 3x
[(x³)² - 1]/[(x + 1)(x - 1)(x² + x + 1)] = [(x³ + 1)(x³ - 1)]/[(x + 1)(x³ - 1)] = 3x
(x³ + 1)/(x + 1) = [(x + 1)(x² - x + 1)]/(x + 1) = 3x, x² - x + 1 = 3x
x² - 4x + 1 = 0, (x - 2)² = 3 = (√3)², x - 2 = ± √3; x = 2 ± √3
Answer check:
(x⁷ + x⁵ + x³)/(x⁶ + x⁵ + x⁴) = 81/27; x² - x + 1 = 3x
x = 2 ± √3: x² - 4x + 1 = 0, x² - x + 1 = 3x; Confirmed
Final answer:
x = 2 + √3 or x = 2 - √3

[@user-xh3ih4ks9y]

原式：（x^2+1+x^-2)/(x+1+x^-1)=3
x^2+1+x^-2=3(x+1+x^-1)

[@aditya0710]

It was unsmart to keep rewriting 81/27, when that's just 3

[@SidneiMV]

(x² + 1 + 1/x²)/(x + 1 + 1/x) = 3
x² + 1 + 1/x² = 3(x + 1 + 1/x)
(x + 1/x)² - 3(x + 1/x) - 4 = 0
x + 1/x = u
u² - 3u - 4 = 0
(u - 4)(u + 1) = 0
u - 4 = 0 => u = 4
x + 1/x = 4
x² - 4x + 1 = 0
x = (4 ± 2√3)/2
*x = 2 ± √3*
u + 1 = 0 => u = -1
x + 1/x = -1
x² + x + 1 = 0
*x = (-1 ± i√3)/2*

[@walterwen2975]

Please be advised that after the preliminary simplified step, the equation becomes;
(x⁴ + x² + 1)/(x² + x + 1) = 3x: x² + x + 1 ≠ 0

[@SidneiMV]

@@walterwen2975 don't be a moron please. LHS: both parts - numerator and denominator - were divided by x⁵