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If a gt 0, the least value of (a^3+a^2+a...

If `a gt 0`, the least value of `(a^3+a^2+a+1)^2` is

A

`64a^2`

B

`16a^4`

C

`16a^3`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have
`(a^(3) + 1)/(2) ge sqrt(a^(3) xx 1)`
and `(a^(2) + a^(1))/(2) ge sqrt(a^(2) a^(1))`
Adding, we get
`(a^(3) + a^(2) + a + 1)/(2) ge 2 sqrt(a^(3))`
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