Question

if x = 2 + root 3 find the value of x square + 1 / x square

Answer 1

Hey dear here is your answer!!!!

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Answer 2

Here is your solution

Given :-

x=2+√3

Now

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

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

Hope it helps you