Question

if x=(4-root15),find the value of (+1/x)​

Answer 1

Explanation:

$\bold{Correct \: Question -} \\ \\ If \: x = 4 - \sqrt{15} \: then \: find \: the \: value \: of \: x + \frac{1}{x}$

$\bold{Given - } \\ </p><p> x = 4 - \sqrt{15} \\ \\ \bold{To \: find - } \\ Value \: of \: x + \frac{1}{x} \\ \\ \leadsto (4 - \sqrt{15} ) + \frac{1}{(4 - \sqrt{15} )} \\ \\ \leadsto\frac{(4 - \sqrt{15}) {}^{2} + 1}{(4 - \sqrt{15}) } \\ \\ \leadsto\frac{16 - 8 \sqrt{15} + 15 + 1}{(4 - \sqrt{15}) } \\ \\ \leadsto \frac{32 - 8 \sqrt{15} }{(4 - \sqrt{15}) } \\ \\ \leadsto\frac{8 \cancel{(4 - \sqrt{15})} }{ \cancel{(4 - \sqrt{15} )}} \\ \\ \bold{= 8 }$