Question

if x-1/x=2,find x^4+1/x^4

Answer 1

Given, x - 1 / x = 2

   Square on both sides,

( x - 1 / x)^2= 2^2

( x )^2 + ( 1 / x )^2 - 2( x * 1 / x ) = 2 * 2

x^2 + 1 / x^2 - 2 = 4

x^2 + 1 / x^2 = 4  + 2

x^2 + 1 / x^2 = 6

   Again square on both sides

( x^2 + 1 / x^2 )^2 = 6^2

( x^2 )^2 + ( 1 / x^2 )^2 + 2( x^2 * 1 / x^2 ) = 36

x^4 + 1 / x^4 + 2 = 36

x^4 + 1 / x^4 = 36 - 2

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

Therefore the value of x^4 + 1 / x^4 is 34