Question

If x =(4-square15) ,find the value value of (x +1/x)​

Answer 1

Answer:

$x = 4 - \sqrt{15} \\ = > \frac{1}{x} = \frac{1}{4 - \sqrt{15} } = \frac{1}{4 - \sqrt{15} } \times \frac{4 + \sqrt{15} }{4 + \sqrt{15} } \\ = > \frac{1}{x} = \frac{4 + \sqrt{15} }{ {4}^{2 } - { \sqrt{15} }^{2} } = \frac{4 + \sqrt{15} }{16 - 15} \\ = > \frac{1}{x} = 4 + \sqrt{15} \\ now \\ x + \frac{1}{x} = 4 - \sqrt{15} + 4 + \sqrt{15} \\ = > x + \frac{1}{x} = 8$

the answer is 8.