First slide

Theory of expressions

Question

$The number of solutions of the equation (3 | x | - 3)^{2} = | x | + 7 which belong to the domain of \sqrt{x (x - 3)} is$

Moderate

A

0
B

2
C

4
D

infinite

Solution

$\begin{array}{l} Domain of \sqrt{x (x - 3)} is x \in (- \infty, 0] \cup [3, \infty) \\ Now, (3 | x | - 3)^{2} = | x | + 7 \\ \Rightarrow 9 | x |^{2} - 19 | x | + 2 = 0 \\ \Rightarrow (9 | x | - 1) (| x | - 2) = 0 \\ \Rightarrow | x | = \frac{1}{9} or | x | = 2 \end{array}$
$\begin{array}{l} \Rightarrow x = - \frac{1}{9} or x = - 2 \\ Hence, there are 2 solutions to the given equation. \end{array}$

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