Question

If `a ,b ,c` are non-zero real numbers, then the minimum value of the expression `(((a^4 3a^2+1)(b^4+5b^2+1)(c^4+7c^2+1))/(a^2b^2c^2))` is not divisible by prime number.

Answer 1

Correct Answer - 315
We have `((a^(4)+3a^(2)+1)/a^(2))((b^(2)+5b^(2)+1)/(b^(2)))((c^(4)+7c^(2)+1)/(c^(2)))`
`=(a^(2)+(1)/(a^(2))+3)(b^(2)+(1)/(b^(2))+5)(c^(2)+(1)/(c^(2))+7)`
`=((a-(1)/(a))^(2)+5)((b-(1)/(b))^(2)+7)((c-(1)/(c))^(2)+9)`
So, minimum value is `5xx7xx9=315`.