Question

If x - 1/x = 2 then find the value of x^4+1/x^4​

Answer 1

this is the correct answer (34).

Answer 2

$\huge\rm\color{lightcoral}{Solution}$

Given that $\:\sf{x - \frac{1}{x} = 2 }$

To find : $\sf{{x}^{4} + \frac{1}{ {x}^{4} } }$

$\sf{{(x - \frac{1}{x} )}^{2} = {2}^{2} }$

$\sf {x}^{2} + \frac{1}{ {x}^{2} } - 2 = 4$

$\sf {x}^{2} + \frac{1}{ {x}^{2} } = 4 + 2$

$\sf {x}^{2} + \frac{1}{ {x}^{2} } = 6$

squaring on both sides

$\sf{ ({x}^{2} + \frac{1}{ {x}^{2} } )}^{2} = {6}^{2}$

$\sf {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 36$

$\sf {x}^{4} + \frac{1}{ {x}^{4} } = 36 - 2$

$\fbox{\sf {x}^{4} + \frac{1}{ {x}^{4} } = 34}$