Question

please solve it. please very fast​

Answer 1

Explanation:

$Given, x = 3 - \sqrt{5}$

$x^2 = (3-\sqrt{5})^2 = 3^2 -2(3)(\sqrt{5})+(\sqrt{5})^2 = 9 - 6\sqrt{5}+5 = 14 - 6\sqrt{5}$

$(\frac{4}{x} )=\frac{4}{3-\sqrt{5}} = \frac{4(3+\sqrt{5})}{9 - 5} = \frac{4(3+\sqrt{5})}{4} = 3 +\sqrt{5}$

Hence,

$(\frac{4}{x})^2 = (3+\sqrt{5})^2 = 9 + 6\sqrt{5} + 5 = 14 + 6\sqrt{5}$

Therefore,

$x^2 + (\frac{4}{x})^2 = 14 - 6\sqrt{5} + 14 + 6\sqrt{5} = 28$

Answer: 28

I hope this answer helps. :D