Question

if x=3+2√2, find the value of x²+1/x²​

Answer 1

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$x = 3 + 2 \sqrt{2} \\ \frac{1}{x} = \frac{1}{3 + 2 \sqrt{2} } \\ = \frac{1}{3 + 2 \sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } \\ = \frac{3 - 2 \sqrt{2} }{9 - 8} = 3 - 2 \sqrt{2} \\ x + \frac{1}{x} = 6 \\ ( {x + \frac{1}{x} })^{2} = 36 \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 36 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 34$