Question:
The number of solutions to the equation $|x|\left(6 x^{2}+1\right)=5 x^{2}$ is
Correct Answer: 5
case I: x=0.
Clearly, $x=0$ satisfy the equation.
case II: x>0
$|x|\left(6 x^{2}+1\right)=5 x^{2}$
$\Rightarrow x\left(6 x^{2}+1\right)=5 x^{2}$
$\Rightarrow 6 x^{2}+1-5 x=0$
On solving the quadratic equation, we get $x=\frac{1}{2},\frac{1}{3}$ (both valid)
Case III: x<0
$|x|\left(6 x^{2}+1\right)=5 x^{2}$
$\Rightarrow \quad-x\left(6 x^{2}+1\right)=5 x^{2}$
$\Rightarrow \quad 6 x^{2}+5 x+1=0$
On solving the quadratic equation, we get $x=\frac{-1}{2}\text{ ,}\frac{-1}{3}$ (both valid)
Hence there are 5 solutions.
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