If `a, b, c` are non-zero than minimumm value of expression
`(((a^(4)+3a^(2)+1)(b^(4)+5b^(2)+1)(c^(4)+7c^(2)+1))/(a^(2)b^(2)c^(2)))` equals `pqr` find `p + q+ r`.

Answer

9

Explanation

`:'((a^(4)+3a^(2)+1)/(a^(2)))((b^(4)+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)`
`:.` minimum is at `a = b = c = 1`
minimum value `= 5.7.9 = 315 = pqr`
`p + q+ r = 3 + 1 + 5 = 9`