MCQ
If $3\text{x}+\frac{2}{\text{x}}=7,$ than $\Big(9\text{x}^2-\frac{4}{\text{x}^2}\Big)=$
- A$25$
- ✓$35$
- C$30$
- D$49$
✓
Answer
Correct option: B.
$35$
$\Rightarrow3\text{x}+\frac{2}{\text{x}}=7$
Now, $3\text{x}^2+2-7\text{x}=0$
$\Rightarrow3\text{x}^2-6\text{x}-\text{x}+2=0$
$\Rightarrow(\text{x}-2)(3\text{x}-1)=0$
$\Rightarrow\text{x}=2$ or $\text{x}=\frac{1}{4}$ (neglected)
$\Rightarrow3\text{x}-\frac{2}{\text{x}}=6-1=5$
$\Rightarrow3\text{x}+\frac{2}{\text{x}}=6+1=7$
Now,
$(3\text{x})^2-\Big(\frac{2}{\text{x}}\Big)^2=\Big(3\text{x}-\frac{2}{\text{x}}\Big)\Big(3\text{x}+\frac{2}{\text{x}}\Big)$
$\Rightarrow(3\text{x})^2-\Big(\frac{2}{\text{x}}\Big)^2=5(7)=35$
Now, $3\text{x}^2+2-7\text{x}=0$
$\Rightarrow3\text{x}^2-6\text{x}-\text{x}+2=0$
$\Rightarrow(\text{x}-2)(3\text{x}-1)=0$
$\Rightarrow\text{x}=2$ or $\text{x}=\frac{1}{4}$ (neglected)
$\Rightarrow3\text{x}-\frac{2}{\text{x}}=6-1=5$
$\Rightarrow3\text{x}+\frac{2}{\text{x}}=6+1=7$
Now,
$(3\text{x})^2-\Big(\frac{2}{\text{x}}\Big)^2=\Big(3\text{x}-\frac{2}{\text{x}}\Big)\Big(3\text{x}+\frac{2}{\text{x}}\Big)$
$\Rightarrow(3\text{x})^2-\Big(\frac{2}{\text{x}}\Big)^2=5(7)=35$
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