First slide

Theory of equations

Question

The number of solutions of the equation $x^{2} - 4 | x | - 2 = 0$ is

Moderate

A

1
B

2
C

3
D

4

Solution

$\begin{array}{l} | x |^{2} - 4 | x | - 2 = 0 \\ \Rightarrow (| x | - 2)^{2} = 6 \Rightarrow | x | - 2 = \pm \sqrt{6} \\ \Rightarrow | x | = 2 \pm \sqrt{6} \\ As | x | > 0, | x | = 2 + \sqrt{6} \\ \Rightarrow x = \pm (2 + \sqrt{6}) \end{array}$
$∴$ there are two values of x.

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