State true or false? Give reason?

If a + b + c = 81 , the minimum value of a^10 + b^10 + c^10 is (81)^10.

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- Aug 24th 2008, 12:15 AMpuneetminimum value
State true or false? Give reason?

If a + b + c = 81 , the minimum value of a^10 + b^10 + c^10 is (81)^10. - Aug 24th 2008, 01:16 AMwingless
False. Taking $\displaystyle a=b=c=27$ makes $\displaystyle a^{10}+b^{10}+c^{10} = 3\cdot 27^{10}$ which is less than $\displaystyle 81^{10}$.

Where did you see this question? - Aug 24th 2008, 02:00 AMpuneetignou
It was in my ignou assignment.

- Aug 24th 2008, 02:30 AMwingless
OK. No problem as long as disproving is enough.