If x+15=4, then x+1 x = - Vidyadip

MCQ

If $\text{x}+\sqrt{15}=4,$ then $\text{x}+\frac{1}{\text{x}}=$

A
$2$
B
$4$
✓
$8$
D
$1$

✓

Answer

Correct option: C.

$8$

$\text{x}+\sqrt{15}=4$
$=\text{x}=4-\sqrt{15}\Rightarrow\frac{1}{\text{x}}=\frac{1}{4-\sqrt{15}}$
$\frac{1}{\text{x}}=\frac{1}{4-\sqrt{15}}\times\frac{4+\sqrt{15}}{4+\sqrt{15}}=\frac{4+\sqrt{15}}{(4)^2-\big(\sqrt{15}\big)^2}\\ \ =\frac{4+\sqrt{15}}{16-15}=4+\sqrt{15}$
Now, $\text{x}+\frac{1}{\text{x}}=4-\sqrt{15}+4+\sqrt{15}=8$
Hence, correct option is $(c)$.

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