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  4. If a , b , c are non-zero real numbers then the minimum value of the expression (((a8+4 a4+1)(b4+3 b2+1)(c2+2 c+2)/a4 b2)) equals

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Q. If $a , b , c$ are non-zero real numbers then the minimum value of the expression $\left(\frac{\left(a^8+4 a^4+1\right)\left(b^4+3 b^2+1\right)\left(c^2+2 c+2\right)}{a^4 b^2}\right)$ equals

Complex Numbers and Quadratic Equations

Solution:

$E=\left(a^4+4+\frac{1}{a^4}\right)\left(b^2+3+\frac{1}{b^2}\right)\left((c+1)^2+1\right)$
$E _{\min }=(6)(5)(1)=30$