MCQ
If $\text{x}=2+\sqrt{3}$ then $\text{x}+\frac{1}{\text{x}}=$
- A4
- B5
- C-4
- D-5
✓
Answer
- 4
Solution:
$\text{x}+\frac{1}{\text{x}}$
$\Rightarrow\frac{\text{x}^2+1}{\text{x}}$
Now put, $\text{x}=2+\sqrt{3}$
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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