Rajasthan BoardEnglish MediumSTD 9MATHSPolynomials1 Mark
Question
If $3\text{x}+\frac{2}{\text{x}}=7,$ then $\Big(9\text{x}^2-\frac{4}{\text{x}^2}\Big)=$
✓
Answer
35 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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