MCQ
If $x=1+\sqrt{7}$, then $-\frac{6}{x}$ is equal to
- A$1+\sqrt{7}$
- ✓$1-\sqrt{7}$
- C$\sqrt{7}$
- D$-\frac{6}{\sqrt{7}}$
✓
Answer
Correct option: B.
$1-\sqrt{7}$
(b)
We have, $x=1+\sqrt{7}$
$\therefore$ $ -\frac{6}{x}=\frac{6}{1+\sqrt{7}}=\frac{-6(1-\sqrt{7})}{(1+\sqrt{7})(1-\sqrt{7})}=\frac{-6(1-\sqrt{7})}{1-7}=1-\sqrt{7} $
We have, $x=1+\sqrt{7}$
$\therefore$ $ -\frac{6}{x}=\frac{6}{1+\sqrt{7}}=\frac{-6(1-\sqrt{7})}{(1+\sqrt{7})(1-\sqrt{7})}=\frac{-6(1-\sqrt{7})}{1-7}=1-\sqrt{7} $
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