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If a >0, then least value of (a^3+a^2+a+...

If `a >0,` then least value of `(a^3+a^2+a+1)^2` is (a)`64 a^2` (b)`16 a^4` (c)`16 a^3` (d)d. none of these

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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CENGAGE ENGLISH-INEQUALITIES INVOLVING MEANS -EXERCISES (Single Correct answer type)
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  7. If the product of n positive numbers is n^n , then their sum is a posi...

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  14. If a ,b ,c in R^+, t h e n(b c)/(b+c)+(a c)/(a+c)+(a b)/(a+b) is alwa...

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  15. If a ,b ,c in R^+t h e n(a+b+c)(1/a+1/b+1/c) is always geq12 geq9 lt...

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  20. If a >0, then least value of (a^3+a^2+a+1)^2 is (a)64 a^2 (b)16 a^4 ...

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