Question

If x - 1/x =2 then find thr value of x power 4 +1/xpower 4

Answer 1

Given

$x - \dfrac{1}{x} = 2$

To Find

The value of $x^4\:+\: \dfrac{1}{x^4}$

Calculations

$x\:-\: \dfrac{1}{x}\:=\:2$

Squaring both sides,we get

$\implies \:x^2\:-\:2\:+\: \dfrac{1}{x^2}\:=\:4$

Transposing 2 to other side,we get :-

$\implies \: x^2\:+\: \dfrac{1}{x^2}\:=\:4\:+\:2$

$\implies \: x^2\:+\: \dfrac{1}{x^2}\:=\:6$

Again, squaring both sides,we get

$\implies \: x^4\:+2\:+\: \dfrac{1}{x^4}\:=\: 36$

Transposing 4 to other side,we get

$\implies \: x^4\:+\: \dfrac{1}{x^4}\:=\:36-\:2$

$\implies \: x^4\:+\: \dfrac{1}{x^4}\:=\:34$

Hence,$\boxed{ \: x^4\:+\: \dfrac{1}{x^4}\:=\:34}$

Answer 2

Given

$x - \dfrac{1}{x} = 2$

$</p><p>To Find \\ </p><p>The \: value \: of \: x^4\:+\: \dfrac{1}{x^4}x$

Calculations

$x\:-\: \dfrac{1}{x}\:=\:2x</p><p>$

Squaring both sides,we get

$\implies \:x^2\:-\:2\:+\: \dfrac{1}{x^2}\:=\:4$

Transposing 2 to other side,we get :-

$</p><p>\implies \: x^2\:+\: \dfrac{1}{x^2}\:=\:4\:+\:2$

$\implies \: x^2\:+\: \dfrac{1}{x^2}\:=\:6$

Again, squaring both sides,we get

$\implies \: x^4\:+2\:+\: \dfrac{1}{x^4}\:=\: 36$

Transposing 4 to other side,we get

$\implies \: x^4\:+\: \dfrac{1}{x^4}\:=\:36-\:2$

$\implies \: x^4\:+\: \dfrac{1}{x^4}\:=\:34$

Hence

$,\boxed{ \: x^4\:+\: \dfrac{1}{x^4}\:=\:34} </p><p>$