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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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?
It was in my ignou assignment.
OK. No problem as long as disproving is enough.
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