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JEE Previous Year Question

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

Topic: JEE PYQ

Answer: D. Full step-by-step solution below.

A $2$
B $3$
C $1$
D $4$

Correct answer: D

Solution

(d) Consider \frac{1}{x} = α x > 0 (9 α^{2} - 9 α + 2) (2 α^{2} - 7 α + 3) = 0 (3 α - 2) (3 α - 1) (α - 3) (2 α - 1) = 0 α = \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, 3 x = 9, 4, \frac{9}{4}, \frac{1}{9} So, no. of solutions = 4

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