MCQ
If $\text{x}+\frac{1}{\text{x}}=5,$ then $\text{x}^2+\frac{1}{\text{x}^2}=$
- ✓$23$
- B$10$
- C$27$
- D$25$
✓
Answer
Correct option: A.
$23$
Using, $(\text{a}+\text{b})^2=\text{a}^2+\text{b}^2+2\text{ab}$
$\Big(\text{x}+\frac{1}{\text{x}}\Big)^2=\text{x}^2+\Big(\frac{1}{\text{x}^2}\Big)+2\text{x}\frac{1}{\text{x}}$
$\Rightarrow(5)^2=\text{x}^2+\Big(\frac{1}{\text{x}^2}\Big)+2$
$\Rightarrow\text{x}^2+\Big(\frac{1}{\text{x}^2}\Big)=25-2$
$\Rightarrow\text{x}^2+\Big(\frac{1}{\text{x}^2}\Big)=23$
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