Question

Solve : $x^2-2|x|-3=0$

Answer 1

We can also solve this problem as in problem 33,34 or 42 by considering two cases (a) x < 0 (b) $x\ge 0$ . Another method to solve this equation is an given below :
Put $|x|=y.$ Then $x^2=|x{|}^2=y^2$
Hence the given equation can be written as
$y^2-2y-3=0$ or $(y-3)(y+1)=0$
This gives $|x|=y=3$ or -1 of which $|x|=-1$ is meaningless .
and $|x|=3$ gives $x=\pm 3,$
which is the required solution of the original equation.