Question

i will mark you as brainlist pls help guys

Answer 1

$Given : x = 7 + 5\sqrt{2}$

$= > \frac{1}{x} = \frac{1}{7 + 5\sqrt{2}} * \frac{7 - 5\sqrt{2}}{7 - 5\sqrt{2}}$

$= > \frac{7 - 5\sqrt{2}}{(7)^2 - (5\sqrt{2})^2}$

$= > \frac{7 - 5\sqrt{2}}{49 - 50}$

$= > \frac{7 - 5\sqrt{2}}{-1}$

$= > 5\sqrt{2} - 7$

Now,

$= > x + \frac{1}{x} = 7 + 5\sqrt{2} + 5\sqrt{2} - 7$

$= > 10\sqrt{2}$

On squaring both sides, we get

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

$= > x^2 + \frac{1}{x^2} + 2 * x * \frac{1}{x} = 200$

$= > x^2 + \frac{1}{x^2} + 2 = 200$

$= > x^2 + \frac{1}{x^2} = 198$

Hope this helps!