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4-2.Quadratic Equations and Inequations
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How many positive real numbers $x$ satisfy the equation $x^3-3|x|+2=0$ ?
A
$1$
B
$3$
C
$4$
D
$6$
(KVPY-2009)
Solution
(a)
We have,
Case $I$ $x > 0 \quad x^3-3|x|+2=0$
$\therefore \quad x^3-3 x+2=0$
$\Rightarrow \quad(x-1)(x-1)(x+2)=0$
$\Rightarrow x=1,-2$
$\text { Since, } x > 0$
$\therefore x \neq-2$
$x=1$
Case $II$ $x < 0$
$\therefore \quad x^3+3 x+2=0$
Graph of $x^3+3 x+2$
Clearly, from graph.
It has one solution lie between $(-1,0)$.
$\therefore$ Positive value of $x=1$
Hence, only one solutions.
Standard 11
Mathematics
