Question

If equal to 4-under root 15, find the value of xsq + 1/xsq

Answer 1

Hi friend ✋✋✋✋
--------------
Your answer
--------------------

Given that : - x = 4 - √5

To find : - x² + 1/x² = ?

Now,
----------

$x = 4 - \sqrt{15} \\ \\ \frac{1}{x} = \frac{1}{4 - \sqrt{15} } \\ rationalising \: the \: denominator \\ \\ \frac{1}{x} = \frac{1}{(4 - \sqrt{15} )} \times \frac{(4 + \sqrt{15}) }{(4 + \sqrt{15}) } \\ \\ = > \frac{1}{x} = \frac{4 + \sqrt{15} }{(4) {}^{2} - ( \sqrt{15} ) {}^{2} } \\ \\ = > \frac{1}{x} = \frac{4 + \sqrt{15} }{16 - 15 } \\ \\ \frac{1}{x} = \frac{4 + \sqrt{15} }{1} = 4 + \sqrt{15}$
Then,
----------

$x + \frac{1}{x} = 4 - \sqrt{15} + 4 + \sqrt{15} \\ \\ = > x + \frac{1}{x} = 8 \\ \\ (x + \frac{1}{x} ) {}^{2} = (8) {}^{2} \\ \\ = > x {}^{2} + \frac{1}{x {}^{2} } + 2 = 64 \\ \\ = > x {}^{2} + \frac{1}{x {}^{2} } = 64 - 2 \\ \\ = > x {}^{2} + \frac{1}{x {}^{2} } = 62$
HOPE IT HELPS