An algebra problem by Yash Singhal

Algebra Level 4

Find the sum of all values of x x that satisfy the equation: x x 5 − 37 x 4 + 7 x 3 + 84 x 2 + 2 x + 9 = 1 x^{x^{5}-37x^{4}+7x^{3}+84x^{2}+2x+9}=1


The answer is 37.

Yash Singhal by Yash Singhal , 22, India

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2 solutions

Dhruva Kothari
Sep 18, 2014

let alpha + beta + gamma + delta + phi =-b/a
therefore -(-37)/1 = 37

2 Helpful 0 Interesting 0 Brilliant 0 Confused

copied question!!! solutions are 1,-1 and sum of the roots in polynomial=37, their sum is 37

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Exactly, x α = x β \color{#D61F06}{x^{\alpha}=x^{\beta}} doesn't necessarily implies α = β \color{#3D99F6}{\alpha=\beta} in case x ϵ { − 1 , 0 , 1 } x\,\,\epsilon\,\,\left\{-1,0,1\right\} .

Aditya Sky - 5 years ago

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