Question:
If $x=\frac{\sqrt{7}}{5}$ and $\frac{5}{x}=p \sqrt{7}$ then the value of $p$ is
(a) $\frac{7}{25}$
(b) $\frac{25}{7}$
(c) $\frac{7}{15}$
(d) $\frac{15}{7}$
Solution:
$\frac{5}{x}=p \sqrt{7}$
$\Rightarrow \frac{5}{\frac{\sqrt{7}}{5}}=p \sqrt{7} \quad\left(\because x=\frac{\sqrt{7}}{5}\right)$
$\Rightarrow \frac{5 \times 5}{\sqrt{7}}=p \sqrt{7}$
$\Rightarrow \frac{25}{\sqrt{7}}=p \sqrt{7}$
$\Rightarrow \frac{25}{\sqrt{7} \times \sqrt{7}}=p$
$\Rightarrow \frac{25}{7}=p$
$\therefore$ The value of $p$ is $\frac{25}{7}$.
Hence, the correct option is (b).
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