Question

lif x+1/x=3
thenx²+1/x²​

Answer 1

$\pink{x + \frac{1}{x} = 3 } \\ \\ \blue{sq. \: \: on \: \: b.s} \\ \\ {(x + \frac{1}{x} })^{2} = {3}^{2} \\ \\ {x}^{2} + 2x \times \frac{1}{x} + \frac{1}{ {x}^{2} } = 9 \\ \\ {x}^{2} + 2 + \frac{ {1}^{2} }{ {x}^{2} } = 9 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 9 - 2\\ \\ \green{{x}^{2} + \frac{1}{ {x}^{2} } = 7}$