If 3x+2 x =7, then (9x^2-4 x^2 )= 1. 25 2. 35 3. 49 4. 30

Question

If $3\text{x}+\frac{2}{\text{x}}=7,$ then $\Big(9\text{x}^2-\frac{4}{\text{x}^2}\Big)=$

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Answer

Solution:
$\Big(3\text{x}+\frac{2}{\text{x}}\Big)^2=9\text{x}^2+\frac{4}{\text{x}^2}+12\ ...(1)$
$\Big(3\text{x}-\frac{2}{\text{x}}\Big)^2=9\text{x}^2+\frac{4}{\text{x}^2}-12\ ...(2)$
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).

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