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JEE Main 202529 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
29 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2025 · 29 January · Morning Shift · Mathematics · Quadratic Equation

The number of solutions of the equation (((9)/(x)- 9 x +2)((2)/(x)-...

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:

Options

  1. A2
  2. B3
  3. C1
  4. D4

Correct answer

D. 4

Step-by-step solution

Consider 1x=αx>0\frac{1}{\sqrt{\mathrm{x}}}=\alpha \quad \mathrm{x}>0{9α2−9α+2}{2α2−7α+3}=0(3α−2)(3α−1)(α−3)(2α−1)=0α=13,12,23,3x=9,4,94,19\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}$So,no.ofsolutionsSo, no. of solutions=4$
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