Question

if x+1/x/x-1/x=2 then find x square + 1/x Square​

Answer 1

Answer:

$\frac{x + \frac{1}{x} }{x - \frac{1}{x} } = 2 \\ \\( x + \frac{1}{x} ) = 2(x - \frac{1}{x} ) \\ \\ square \: both \: sides \\ \\ ( x + \frac{1}{x} ) {}^{2} = 4(x - \frac{1}{x} ) {}^{2} \\ \implies\\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 4 {x}^{2} + \frac{4}{ {x}^{2} } - 8 \\ \implies\\ 3 {x}^{2} + \frac{3}{ {x}^{2} } = 2 + 8 = 10 \\ \implies \\ {x}^{2} + \frac{1}{ {x}^{2} } = \frac{10}{3}$