Question

please explain how to solve this

Answer 1

$\\ \\ \sf \: x + \frac{1}{x} = 3$

Using identity (a+b)² = a² + b² + 2ab

⇨ a = x

⇨ b = 1/x

⇨ 2ab = 2 ( x × 1/x )

⇨ 2

$\\ \\ \sf {x}^{2} + \frac{1}{ {x}^{2} } + 2 = ( {3)}^{2} \\ \\ ⇨ \sf {x}^{2} + \frac{1}{ {x}^{2} } = 9 - 2 \\ \\ ⇨ \red{\sf{x}^{2} + \frac{1}{ {x}^{2} } = 7}$