MCQ
If $\text{x}=3+2\sqrt{2},$ than the value of $\text{x}+\frac{1}{\text{x}}$ is:
- ✓6
- B$0$
- C$3$
- D$1$
✓
Answer
Correct option: A.
6
$\text{x}+\frac{1}{\text{x}}$
$\Rightarrow\frac{\text{x}^2+1}{\text{x}}$
Put the value of $x,$
$\Rightarrow\frac{(3+2\sqrt{2})^2+1}{3+2\sqrt{2}}$
$\Rightarrow\frac{9+8+12\sqrt{2}+1}{3+2\sqrt{2}}$
$\Rightarrow\frac{18+12\sqrt{2}}{3+2\sqrt{2}}$
$\Rightarrow\frac{6(3+2\sqrt{2})}{3+2\sqrt{2}}$
$\Rightarrow6$
$\Rightarrow\frac{\text{x}^2+1}{\text{x}}$
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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