First slide

Theory of equations

Question

The number of roots of the equation
$\sqrt{\frac{x}{x - 3}} + \sqrt{\frac{x - 3}{x}} = \frac{5}{2}, x \neq 0, x \neq 3$ is

Moderate

A

0
B

2
C

3
D

4

Solution

Put $\sqrt{\frac{x}{x - 3}} = t$ to obtain $t + \frac{1}{t} = \frac{5}{2}$
$\Rightarrow t = 2, \frac{1}{2}$
$∴ \sqrt{\frac{x}{x - 3}} = 2, \frac{1}{2} \Rightarrow \frac{x}{x - 3} = 4, \frac{1}{4}$

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