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  4. The minimum value of the sum of real numbers a-5, a-4, 3 a-3, 1, a8 and a10 with a>0 is

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Q. The minimum value of the sum of real numbers $a^{-5}, a^{-4}, 3 a^{-3}, 1, a^{8}$ and $a^{10}$ with $a>0$ is ________

JEE AdvancedJEE Advanced 2011

Solution:

$\frac{ a ^{-5}+ a ^{-4}+ a ^{-3}+ a ^{-3}+ a ^{-3}+ a ^{8}+ a ^{10}+1}{8} \geq 1$ minimum value $=8$.