MCQ
If $x=2+\sqrt{3}$, then $x+\frac{1}{x}$ is equals
- A2
- ✓4
- C$-2 \sqrt{3}$
- D$4-2 \sqrt{3}$
✓
Answer
Correct option: B.
4
(b)
We have,$x=2+\sqrt{3}$
$\therefore \quad \frac{1}{x}=\frac{1}{2+\sqrt{3}}=\frac{2-\sqrt{3}}{(2-\sqrt{3})(2+\sqrt{3})}=\frac{2-\sqrt{3}}{4-3}=2-\sqrt{3}$
Hence, $x+\frac{1}{x}=2+\sqrt{3}+2-\sqrt{3}=4$.
We have,$x=2+\sqrt{3}$
$\therefore \quad \frac{1}{x}=\frac{1}{2+\sqrt{3}}=\frac{2-\sqrt{3}}{(2-\sqrt{3})(2+\sqrt{3})}=\frac{2-\sqrt{3}}{4-3}=2-\sqrt{3}$
Hence, $x+\frac{1}{x}=2+\sqrt{3}+2-\sqrt{3}=4$.
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