Question

If x+1/x=5 then find x²+1/x²=?​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

We are aware of the identity that

${a}^{2} + {b}^{2} = {(a + b)}^{2} - 2ab$

GIVEN

$\displaystyle \: x + \frac{1}{x} = 5$

TO DETERMINE

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

EVALUATION

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

$= \displaystyle \: {(x + \frac{1}{x}) }^{2} - 2 \times x \times \frac{1}{x}$

$= {5}^{2} - 2$

$= 25 - 2$

$= 23$