Question

if x = √3+√2/√3-√2 , find x²+1/x²​

Answer 1

$x = \frac{ \sqrt{3 } + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \\ \frac{1}{x} = \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ x + \frac{1}{x} = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } + \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ = \frac{( { \sqrt{3} + \sqrt{2} })^{2} + ( { \sqrt{3} - \sqrt{2} })^{2} }{3 - 2} \\ = 2(3 + 2) \\ = 10 \\ ( {x + \frac{1}{x} })^{2} = 100 \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 100 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 98$