If a,b,c are non-zero real numbers, then the minimum value of the expression `((a^(8)+4a^(4)+1)(b^(4)+3b^(2)+1)(c^(2)+2c+2))/(a^(4)b^(2))` equals

Options

A. 12
B. 24
C. 30
D. 60

Answer

C

Explanation

Let `P=((a^(8)+4a^(4)+1)(b^(4)+3b^(2)+1)(c^(2)+2c+2))/(a^(4)b^(2))`
`(a^(4)+4+(1)/(a^(4)))(b^(2)+3+(1)/(b^(2))){(c+1)^(2)+1}`
`:.a^(4)+4+(1)/(a^(4))ge6,b^(2)+3+(1)/(b^(2))ge5 " and "(c+1)^(2)+1ge 1`
`[:. x+(1)/(x)ge2 " for "xgt0]`
`:.P ge 6*5*1=30 implies Pge30`
Hence, the required minimum value is 30.