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  4. Number of real solutions of the equation x4+8 x2+16=4 x2-12 x+9 is equal to -

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Q. Number of real solutions of the equation $x^4+8 x^2+16=4 x^2-12 x+9$ is equal to -

Complex Numbers and Quadratic Equations

Solution:

$\left(x^2+4\right)^2=(2 x-3)^2 $
$\Rightarrow x^2+4=\pm(2 x-3) $
$\Rightarrow x^2+2 x+1=0 \text { or } \underbrace{x^2-2 x+7}_{\text {D }< 0}=0 $
$\Rightarrow (x+1)^2=0 \text { or } \text { No solution }$
$\Rightarrow x=-1$
Have only one solution.