MCQ
If $\text{x}^2+\frac{1}{\text{x}^2}=102,$ than $\text{x}-\frac{1}{\text{x}}=$
- A$2$
- B$12$
- ✓$10$
- D$13$
✓
Answer
Correct option: C.
$10$
$\text{x}^2+\frac{1}{\text{x}^2}=102,$
$\Rightarrow(\text{x}^2)+\Big(\frac{1}{\text{x}^2}\Big)-2\times\text{x}\times\frac{1}{\text{x}}=102-2\times\text{x}\times\frac{1}{\text{x}}$
$\Rightarrow\Big(\text{x}-\frac{1}{\text{x}}\Big)^2=100$
$\Rightarrow\text{x}-\frac{1}{\text{x}}=\sqrt{100}=10$
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