Substitution?

Algebra Level 3

Given that x = 2017 6 \large x = \sqrt \frac{2017}{6} . Compute 750 x 6 + 150 x 4 + 30 x 2 5 + 25 x 2 + 125 x 4 \large \dfrac{750x^6 + 150x^4 + 30x^2}{5 + 25x^2 + 125x^4}


The answer is 2017.

Ravneet Singh by Ravneet Singh , 30, India

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1 solution

Zach Abueg
Jul 11, 2017

750 x 6 + 150 x 4 + 30 x 2 125 x 4 + 25 x 2 + 5 = 30 x 2 ( 25 x 4 + 5 x 2 + 1 ) 5 ( 25 x 4 + 5 x 2 + 1 ) = 6 x 2 x 2 = 2017 6 = 2017 \displaystyle \begin{aligned} \frac{750x^6 + 150x^4 + 30x^2}{125x^4 + 25x^2 + 5} & = \frac{30x^2 \left(25x^4 + 5x^2 + 1\right)}{5\left(25x^4 + 5x^2 + 1\right)} \\ & = 6x^2 & \small \color{#3D99F6} x^2 = \frac{2017}{6} \\ & = \boxed{2017} \end{aligned}

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