JEE MAIN - Mathematics (2003 - No. 38)
The number of real solutions of the equation $${x^2} - 3\left| x \right| + 2 = 0$$ is
3
2
4
1
Explicação
$${x^2} - 3\left| x \right| + 2 = 0$$
$$ \Rightarrow {\left| x \right|^2} - 3\left| x \right| + 2 = 0$$
$$\left( {\left| x \right| - 2} \right)\left( {\left| x \right| - 1} \right) = 0$$
$$\left| x \right| = 1,2$$ or $$x = \pm 1, \pm 2$$
$$\therefore$$ No. of solution $$=4$$
$$ \Rightarrow {\left| x \right|^2} - 3\left| x \right| + 2 = 0$$
$$\left( {\left| x \right| - 2} \right)\left( {\left| x \right| - 1} \right) = 0$$
$$\left| x \right| = 1,2$$ or $$x = \pm 1, \pm 2$$
$$\therefore$$ No. of solution $$=4$$