Question

If
x=√7-3√5 then find the value of X +1/x​

Answer 1

Answer:

-4

Step-by-step explanation:

Given :

$x = \sqrt{7} - 3 \sqrt{5}$

$x + \frac{1}{x} = \frac{ {x}^{2} + 1 }{x} \\ \\ = \frac{ (\sqrt{7} - 3 \sqrt{5}) {}^{2} }{ \sqrt{7} - 3 \sqrt{5} } \\ \\ we \: know \: that \: {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ \\ = \frac{ (\sqrt{7} ) {}^{2} + (3 \sqrt{5} ) {}^{2} - 2 \times \sqrt{7} \times 3 \sqrt{5} }{ \sqrt{7} - 3 \sqrt{5} } \\ \\ = \frac{7 + 45 - 36}{ \sqrt{7} - 3 \sqrt{5} } \\ \\ = \frac{16}{ - 4} \\ \\ = - 4$