The number of solutions of the equation (9/x-frac 9 √(x) +2 ) (2/x-frac 7 √(x) +3 )=0 is

Mathematics · Quadratic Equations

JEE Main 2025 — 29 January, Morning Shift — Question 53

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

Consider $\frac{1}{\sqrt{\mathrm{x}}}=\alpha, \quad \mathrm{x}>0$

$\left\{9 \alpha^{2}-9 \alpha+2\right\}\left\{2 \alpha^{2}-7 \alpha+3\right\}=0$

$(3 \alpha-2)(3 \alpha-1)(\alpha-3)(2 \alpha-1)=0$

$\alpha=\frac{1}{3}, \frac{1}{2}, \frac{2}{3}, 3$

$\mathrm{x}=9,4, \frac{9}{4}, \frac{1}{9}$

So, no. of solutions $=4$

Answer key and solution verified before publishing.

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