MCQ
If $3\text{x}+\frac{2}{\text{x}}=7,$ then $\Big(9\text{x}^2-\frac{4}{\text{x}^2}\Big)=$
- A$25$
- ✓$35$
- C$49$
- D$30$
✓
Answer
Correct option: B.
$35$
$\Big(3\text{x}+\frac{2}{\text{x}}\Big)^2=9\text{x}^2+\frac{4}{\text{x}^2}+12\ ...(1)$
$\Big(3\text{x}-\frac{2}{\text{x}}\Big)^2=9\text{x}^2+\frac{4}{\text{x}^2}-12\ ...(2)$
Subtracting eq. $(1)$ from eq. $(2)$. we get
$\Big(3\text{x}-\frac{2}{\text{x}}\Big)^2-\Big(3\text{x}+\frac{2}{\text{x}}\Big)^2=-24$
$\Rightarrow\Big(3\text{x}-\frac{2}{\text{x}}\Big)^2=(7)^2-24=25$
$\Rightarrow3\text{x}-\frac{2}{\text{x}}=5$
Now $\Big(3\text{x}+\frac{2}{\text{x}}\Big)-\Big(3\text{x}-\frac{2}{\text{x}}\Big)=7\times5$
$\Big(9\text{x}^2-\frac{4}{\text{x}^2}\Big)=35$
Hence, correct option is $(b)$.
$\Big(3\text{x}-\frac{2}{\text{x}}\Big)^2=9\text{x}^2+\frac{4}{\text{x}^2}-12\ ...(2)$
Subtracting eq. $(1)$ from eq. $(2)$. we get
$\Big(3\text{x}-\frac{2}{\text{x}}\Big)^2-\Big(3\text{x}+\frac{2}{\text{x}}\Big)^2=-24$
$\Rightarrow\Big(3\text{x}-\frac{2}{\text{x}}\Big)^2=(7)^2-24=25$
$\Rightarrow3\text{x}-\frac{2}{\text{x}}=5$
Now $\Big(3\text{x}+\frac{2}{\text{x}}\Big)-\Big(3\text{x}-\frac{2}{\text{x}}\Big)=7\times5$
$\Big(9\text{x}^2-\frac{4}{\text{x}^2}\Big)=35$
Hence, correct option is $(b)$.
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