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  4. The imaginary roots of the equation (x2+2)2+8 x2=6 x(x2+2) are

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Q. The imaginary roots of the equation $\left(x^2+2\right)^2+8 x^2=6 x\left(x^2+2\right)$ are

Complex Numbers and Quadratic Equations

Solution:

$\left(x^2+2\right)^2+8 x^2=6 x\left(x^2+2\right)$
$\left(x^2+2\right)^2-6 x\left(x^2+2\right)+8 x^2=0$
$x^2+2=\frac{6 x \pm \sqrt{36 x^2-32 x^2}}{2}$
$x^2+2==3 x \pm x$
$x^2+2=4 x, D>0 $ roots are real
$x^2+2=2 x$
$x=1 \pm i$