The number of solutions of the equation ( x 9 − x 9 + 2 ) ( x 2 − x 7 + 3 ) = 0 is:

Consider x 1 = 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 = 3 1 , 2 1 , 3 2 , 3 x = 9 , 4 , 4 9 , 9 1 So, no. of solutions = 4

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Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationTheory of equationsMedium2 minPYQ_2025

MathematicsMediumsingle choice

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

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Solution:

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 $= 4$

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Theory of equations

⏱ 2mℹ️ Source: PYQ_2025

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