Question

if x+1/x=5 then evaluate x^2+1/x*2​

Answer 1

Given that

$\boxed{\underline{\bf{\pink{x+1/x=5}}}}$

To find

$x {}^{2} + \frac{1}{x {}^{2} }$

$\boxed{\boxed{\underline{\huge{\pink{Answer}}}}}$

Squaring both sides

$(x + \frac{1}{x} ) {}^{2} = (5) {}^{2}$

$x {}^{2} + \frac{1}{ {x}^{2} } + 2(x)( \frac{1}{x} ) = 25$

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

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