Question

x-1/x=5 then xsquare -1/xsquare =​

Answer 1

Answer:

$if \: (x + \frac{1}{x} ) = 5 \\ then \: ( {x}^{2} + \frac{1}{ {x}^{2}}) = ?$

Step-by-step explanation:

${(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} \\ ( {x}^{2} + \frac{1}{ {x}^{2} } ) = ?$

${x}^{2} + 2 \times x \times \frac{1}{x} + \frac{1}{{x}^{2} } = {5}^{2} \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 25$

${x}^{2} + \frac{1}{{x}^{2} } = 25 - 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 23$

So answer is 23