Question

if x=2+√3,find the value of x²+1/x²​

Answer 1

Thanks for the question

Answer 2

Answer:

Answer is 14.

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Step-by-step explanation:

Given,

$x = 2 + \sqrt{3} \\ \therefore \: \frac{1}{x} = \frac{1}{2 + \sqrt{3} } \\ = > \frac{1}{x} = \frac{2 - \sqrt{3} }{(2 + \sqrt{3})(2 - \sqrt{3}) } \\ = > \frac{1}{x} = \frac{2 - \sqrt{3} }{ {(2)}^{2} - { (\sqrt{3} )}^{2} } \\ = > \frac{1}{x} = \frac{2 - \sqrt{3} }{4 - 3} \\ = > \frac{1}{x} = \frac{2 - \sqrt{3} }{1} \\ = > \frac{1}{x} = 2 - \sqrt{3}$

$\therefore \: {x}^{2} + \frac{1}{ {x}^{2} } \\ = {(x + \frac{1}{x} )}^{2} - 2.x. \frac{1}{x} \\ = {(2 + \sqrt{3} + 2 - \sqrt{3} )}^{2} - 2 \\ = {(4)}^{2} - 2 \\ = 16 - 2 \\ = 14$