Question

if x=6+√35 find x²-1÷x²

Answer 1

Hello Mate!

$x = 6 + \sqrt{35} \\ {x}^{2} - \frac{1}{ {x}^{2} } = y \\ {x}^{2} = {(6 + \sqrt{35}) }^{2} \\ 36 + 35 + 12 \sqrt{35} \\ 71 + 12 \sqrt{35} \\ \\ \frac{1}{ {x}^{2} } = \frac{1}{71 + 12 \sqrt{35} } \\ \frac{1}{71 + 12 \sqrt{35} } \times \frac{71 - 12 \sqrt{35} }{71 - 12 \sqrt{35} } \\ \frac{71 - 12 \sqrt{35} }{5041 - 5040} = 71 - 12 \sqrt{35} \\ \\ now \: 70 + 12 \sqrt{35} - (71 - 12 \sqrt{35} )\\ = 24 \sqrt{35}$

Hope it helps☺!

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