Question

if x= 1/ √ 3- √ 2then find the value of (x²+1/x²)
please help me guys ​

Answer 1

$x = \frac{1}{ \sqrt{3} - \sqrt{2} } \\ x = \frac{1}{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ x = \frac{ \sqrt{3} + \sqrt{2} }{ 3 - 2 } \\ x = \sqrt{3} + \sqrt{2} \\ \\ \frac{1}{x} = \frac{1}{ \sqrt{3} + \sqrt{2} } \\ \frac{1}{x} = \frac{ \sqrt{3} - \sqrt{2} }{3 - 2} \\ \frac{1}{x} = \sqrt{3} - \sqrt{2} \\ \\ x + \frac{1}{x} = 2 \sqrt{3} \\ ( {x + \frac{1}{x} })^{2} = 12 \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2= 12 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 10$

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