Question

Let `ab=1`, then the minimum value of `(1)/(a^(4))+(1)/(4b^(4))` is
A. `1`
B. `2`
C. `1//4`
D. `1//2`

Answer 1

Correct Answer - A
`(a)` Using `A.M. ge G.M.`, we get
`((1)/(a^(4))+(1)/(4b^(4)))/(2) ge (1)/(2)` (as `ab=1`)
`implies(1)/(a^(4))+(1)/(4b^(4)) ge 1` Hence minimum value of `((1)/(a^(4))+(1)/(4b^(4)))` is `1`