Question

If x -1/x = 2, then find the value of x⁴+1/x⁴​

Answer 1

Answer:-

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

Squaring both sides, we get,

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

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

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

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

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

Squaring both sides, we get,

$\sf \implies({ {x}^{2} + \frac{1}{ {x}^{2} }})^{2} =36$

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

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

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

Hence,

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