Question

x2+1/x2=18 x=✓5+2 pls tell

Answer 1

Here is your answer:

$x = \sqrt{5} + 2 \\ \\ \frac{1}{x} = \frac{1}{ \sqrt{5} + 2 } \times \frac{ \sqrt{5} - 2 }{ \sqrt{5} - 2 } \\ \\ \frac{1}{x} = \frac{ \sqrt{5} - 2 }{( \sqrt{5} ) {}^{2} - (2) {}^{2} } \\ \\ \frac{1}{x = \frac{ \sqrt{5} - 2 }{5 - 4} } \\ \\ \frac{1}{x} = \sqrt{5} - 2$

Now,

$x + \frac{1}{x} = \sqrt{5} + 2 + \sqrt{5} - 2 \\ \\ x + \frac{1}{x} = 2 \sqrt{5} \\ \\ \underline{ \tt squaring \: both \: sides} - \\ \\ (x + \frac{1}{x} ) {}^{2} = (2 \sqrt{5} ) {}^{2} \\ \\ x {}^{2} + \frac{1}{x {}^{2} } + 2 = 20 \\ \\ x {}^{2} + \frac{1}{x {}^{2} } = 20 - 2 \\ \\ \boxed { \bf x {}^{2} + \frac{1}{x {}^{2} } = 18}$

Hence Proved.