Question

please help me answer is highlighted

Answer 1

1/x = 1/(4-√15)
on rationalizing, we get 4 +√15(see pic)
so x +1/x =
4-√15+4+√15
=8(negative and positive √15 get cancelled).

proved
hope it helps

Answer 2

$\huge\green{\mathfrak{solution:}}$
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$x + \sqrt{15} = 4 \\ \\ x = 4 - \sqrt{15}$

now,

$x + \frac{1}{x} \\ \\ 4 - \sqrt{15} + \frac{1}{4 - \sqrt{15} } \\ \\ \frac{16 + 15 - 8 \sqrt{15} + 1 }{4 - \sqrt{15} } \\ \\ \frac{32 - 8 \sqrt{15} }{4 - \sqrt{15} } \\ \\ \frac{8(4 - \sqrt{15} )}{4 - \sqrt{15} } = 8$

$\huge\red{\boxed{8}}$

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