Question

If x = 2+ root 3 , find the value of x square + 1/x square.

Answer 1

2+√3 = x and x^2 + 1/x^2 = 50/7 = 7.14

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