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

Question

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 :

(1) 2

(2) 4

(3) 1

(4) 3

Answer 1

Correct option is (2) 4  

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