Question

X=√3+√2÷√3-√2 find x×x+1÷x×x​

Answer 1

Solution

$x = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \\ \frac{1}{x} = \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ therefore \\ \\ x + \frac{1}{x} = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } + \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ = > x + \frac{1}{x} = \frac{( \sqrt{3} + \sqrt{2} ) {}^{2} + ( \sqrt{3} - \sqrt{2} ) {}^{2} }{ (\sqrt{3} ) {}^{2} - (\sqrt{2} ) {}^{2} } = \frac{2(3 + 2)}{3 - 2} \\ = > x + \frac{1}{x} = 10$

$x {}^{2} + \frac{1}{x {}^{2} } = (x + \frac{1}{x} ) {}^{2} - 2x. \frac{1}{x} \\ = = > x {}^{2} + \frac{1}{x {}^{2} } = 10 {}^{2} - 2 = 98$

Hope this helps u:::::::