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The minimum value of the sum of real num...

The minimum value of the sum of real number `a^(-5),a^(-4),3a^(-3),1,a^8,a n da^(10)w i t ha >0` is

Text Solution

Verified by Experts

The correct Answer is:
8
Using `AM ge GM`
`(a^(-5) + a^(-4) + a^(-3) + a^(-3) + a^(-3) + 1 + a^(8) + a^(10))/(8)`
`ge (a^(-5).a^(-4).a^(-3).a^(-3).1.a^(8).a^(10))^((1)/(8))`
`rArr a^(-5) + a^(-4) + 3a^(-3) + 1 + a^(8) + a^(10) ge 8.1`
Hence, minimum value is 8
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