Question

If x = 5 + 2 root 6 find the value of x2 + 1/x2

Answer 1

Answer:

Hey Mate!!

$x = 5 + 2 \sqrt{6} \\ = > {x}^{2} = {(5 + 2 \sqrt{6}) }^{2} \\ = > {x}^{2} = {5}^{2} + 2(5)(2 \sqrt{6} ) + {(2 \sqrt{6}) }^{2} \\ = > {x}^{2} = 25 + 20 \sqrt{6} + 24 \\ = > \bold{{x}^{2} = 49 +20 \sqrt{6} } \\ \\ \frac{1}{ {x}^{2} } = \frac{1}{49 +20 \sqrt{6}} \\ = > \frac{1}{ {x}^{2} } = \frac{49 - 20 \sqrt{6}}{(49 +20 \sqrt{6})(49 - 20 \sqrt{6})} \\ = > \frac{1}{ {x}^{2} } = \frac{49 - 20 \sqrt{6}}{ {49}^{2} - {(20 \sqrt{6}) }^{2} } \\ = > \frac{1}{ {x}^{2} } = \frac{49 - 20 \sqrt{6}}{2401 - 2400} \\ = > \bold{ \frac{1}{ {x}^{2} } =49 - 20 \sqrt{6}}$

$= > {x}^{2} + \frac{1}{ {x}^{2} } \\ = > 49 + 20 \sqrt{6} + 49 - 20 \sqrt{6} \\ = > \boxed{ \bold{98} }$