Question

if x-1/x = 2, find x⁴+1/x⁴​

Answer 1

Step-by-step explanation:

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Answer 2

$\bold{x-\frac{1}{x}=2}$

Now squaring on both sides , we get ,

$\implies \bold{(x-\frac{1}{x})^2=2^2}\\\\\implies \bold{x^2+\frac{1}{x^2}-2.x.\frac{1}{x}=4}\\\\\implies \bold{x^2+\frac{1}{x^2}=6}$

Now once again squaring on both sides , we get ,

$\implies \bold{(x^2+\frac{1}{x^2})^2=6^2}\\\\\implies \bold{(x^2)^2+(\frac{1}{x^2})^2+2.x^2.\frac{1}{x^2}=36}\\\\\implies \bold{x^4+\frac{1}{x^4}+2=36}\\\\\implies \bold{\bf{\blue{x^4+\frac{1}{x^4}=34}}}$