MCQ
If $\text{x}=3+2\sqrt{2},$ than the value of $\text{x}+\frac{1}{\text{x}}$ is:
- A6
- B0
- C3
- D1
✓
Answer
- 6
Solution:
$\text{x}+\frac{1}{\text{x}}$
$\Rightarrow\frac{\text{x}^2+1}{\text{x}}$
Put the value of x,
$\Rightarrow\frac{(3+2\sqrt{2})^2+1}{3+2\sqrt{2}}$
$\Rightarrow\frac{9+8+12\sqrt{2}+1}{3+2\sqrt{2}}$
$\Rightarrow\frac{18+12\sqrt{2}}{3+2\sqrt{2}}$
$\Rightarrow\frac{6(3+2\sqrt{2})}{3+2\sqrt{2}}$
$\Rightarrow6$
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