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:
Show Hint
- 3
- 1
- 2
- 4
The Correct Option is C
Solution and Explanation
Step 1: The given equation is a product of two factors. For the equation to hold, either one or both factors must be zero.
Step 2: Solve each factor separately: 1. \( \frac{9}{x} - \frac{9}{\sqrt{x}} + 2 = 0 \) 2. \( \frac{2}{x} - \frac{7}{\sqrt{x}} + 3 = 0 \)
Step 3: Solve each of the resulting equations for \( x \), and ensure that the solutions satisfy the conditions of the problem.
Step 4: After solving both equations, you will find that there are 2 distinct solutions for \( x \). Thus, the correct answer is (3).
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