Question

if x=3+√2 find x2 +(1/x2).​

Answer 1

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$\huge\sf\underline\red{Solution}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \small\sf\underline\green{ x = 3 + \sqrt{2} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \small\sf\green{ \frac{1}{x} = \frac{1}{3 + \sqrt{2} } }$

$\small\sf\red{ \frac{1}{3 + \sqrt{2} } \times \frac{3 - \sqrt{2} }{3 - \sqrt{2} } = \frac{3 - \sqrt{2} }{3 - 2} } \\ \\ \small\sf\underline\red{ = 3 - \sqrt{2} }$

$\small\sf\pink{x + \frac{1}{x} = 3 + \sqrt{2} + 3 - \sqrt{2} } \\ \\ \: \: \: \: \: \: \small\sf\underline\pink{3 + 3 = 9}$

$\: \: \: \: \: \: \small\sf\purple{(x + \frac{1}{x}) {}^{2} = (9) {}^{2} = 81} \\ \\ \: \: \: \: \: \: \small\sf\purple{ (x + \frac{1}{x} ) {}^{2} = x {}^{2} + \frac{1}{x {}^{2} } + 2}$

$\small\sf\orange{x {}^{2} + \frac{1}{x {}^{2} } + 2 = 81 } \\ \\ \small\sf\orange{x {}^{2} + \frac{1}{x {}^{2} } = 81 - 2 = 79}$

$\huge\fbox\gray{hope\:its\:helpful!}$

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