The number of solutions of the equation $\left(\frac{9}{x}-\frac{9}{\sqrt{x}}+2\right)\left(\frac{2}{x}-\frac{7}{\sqrt{x}}+3\right)=0$ is:

Question

Aicharya · Accepted Answer

Consider $\frac{1}{\sqrt{\mathrm{x}}}=\alpha \quad \mathrm{x}>0$
$\begin{aligned}
& \left\{9 \alpha^2-9 \alpha+2\right\}\left\{2 \alpha^2-7 \alpha+3\right\}=0 \\ & (3 \alpha-2)(3 \alpha-1)(\alpha-3)(2 \alpha-1)=0 \\ & \alpha=\frac{1}{3}, \frac{1}{2}, \frac{2}{3}, 3 \\ & x=9,4, \frac{9}{4}, \frac{1}{9}
\end{aligned}$
So, no. of solutions $=4$ ,

The number of solutions of the equation…

Solution