Question

if x=5-2root6 find x square+1/x square

Answer 1

Hey friend,
Here is the answer you were looking for:
$x = 5 - 2 \sqrt{6} \\ \\ \frac{1}{x} = \frac{1}{5 - 2\sqrt{6} } \\ \\ on \: rationalizing \: the \: denominator \: we \: get \\ \\ \frac{1}{x} = \frac{1}{5 - 2 \sqrt{6} } \times \frac{5 + 2 \sqrt{6} }{5 +2 \sqrt{6} } \\ \\ using \: the \: identity \\ \\ \frac{1}{x} = \frac{5 + 2\sqrt{6} }{ {(5)}^{2} - {(2 \sqrt{6}) }^{2} } \\ \\ \frac{1}{x} = \frac{ 5 + 2\sqrt{6} }{25 - 24} \\ \\ \frac{1}{x} = 5 + 2 \sqrt{6} \\ \\ x + \frac{1}{x} = (5 - 2 \sqrt{6} ) + (5 + 2 \sqrt{6} ) \\ \\ x + \frac{1}{x} = 5 - 2 \sqrt{6} + 5 + 2 \sqrt{6} \\ \\ x + \frac{1}{x} = 5 + 5 \\ \\ x + \frac{1}{x} = 10 \\ \\ squaring \: both \: the \: side \\ \\ {(x + \frac{1}{x} )}^{2} = {(10)}^{2} \\ \\ {x}^{2} + { (\frac{1}{x} )}^{2} + 2 \times x \times \frac{1}{x} = 100 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 100 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 100 - 2 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 98$

Hope this helps!!!

@Mahak24

Thanks...
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