Question

If X = 6-√35, find the value of x² + 1/x²​

Answer 1

Answer:

$x = 6 - \sqrt{35} \\ \frac{1}{x} = \frac{1}{6 - \sqrt{35} } \\ = \frac{ 6 + \sqrt{35} }{(6 - \sqrt{35)} (6 + \sqrt{35)} } = \frac{6 + \sqrt{35} }{36 - 35} = 6 + \sqrt{35} \\ {x}^{2} + \frac{1}{ {x}^{2} } = (6 - \sqrt{35)^{2} } + (6 + \sqrt{35) ^{2} } \\ = 36 + 35 - 12 \sqrt{35} + 36 + 35 + 12 \sqrt{35} \\ = 71 + 71 \\ = 142$

142 is the correct answer

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