Question

If x=3+2√2,find the value of x square +1/x square

Answer 1

$x = 3 + 2 \sqrt{2} \\ \\ \frac{1}{x} = \frac{1}{3 + 2 \sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } \\ \\ \frac{1}{x} = \frac{3 - 2 \sqrt{2} }{ 9 - 8} \\ \\ \frac{1}{x} = 3 - 2 \sqrt{2}$

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${x}^{2} = {(3 + 2 \sqrt{2} )}^{2} \\ \\ = 9 + 8 + 12 \sqrt{2} \\ \\ = 17 + 12 \sqrt{2}$
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${( \frac{1}{x}) }^{2} = {(3 - 2 \sqrt{2} )}^{2} \\ \\ = 9 + 8 - 12 \sqrt{2} \\ \\ = 17 - 12 \sqrt{2}$
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${x}^{2} + ( { \frac{1}{x}) }^{2} = 17 + 12 \sqrt{2} + 17 - 12 \sqrt{2} \\ \\ = 17 + 17 \\ \\ = 34$