MCQ
If $x=2+\sqrt{3}$, then $x+\frac{1}{x}=$
- ✓$4$
- B$-5$
- C$-4$
- D$5$
✓
Answer
Correct option: A.
$4$
$x+\frac{1}{x}$
$\Rightarrow \frac{x^2+1}{x}$
now, put $x=2+\sqrt{3}$
we have, $\frac{(2+\sqrt{3})^2+1}{2+\sqrt{3}}$
$\Rightarrow \frac{4+3+2(2 \sqrt{3})+1}{2+\sqrt{3}}$
$\Rightarrow \frac{8+4 \sqrt{3}}{2+\sqrt{3}}$
$\Rightarrow \frac{4(2+\sqrt{3})}{2+\sqrt{3}}$
$=4$
$\Rightarrow \frac{x^2+1}{x}$
now, put $x=2+\sqrt{3}$
we have, $\frac{(2+\sqrt{3})^2+1}{2+\sqrt{3}}$
$\Rightarrow \frac{4+3+2(2 \sqrt{3})+1}{2+\sqrt{3}}$
$\Rightarrow \frac{8+4 \sqrt{3}}{2+\sqrt{3}}$
$\Rightarrow \frac{4(2+\sqrt{3})}{2+\sqrt{3}}$
$=4$
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