The minimum value of the sum of real numbers `a^-5, a^-4, 3a^-3, 1,a^8` and `a^10` with `agt 0` is __________.

Options

A. 6
B. 7
C. 8
D. 9

Answer

C

Explanation

Using `AMgeGM,` we have
`(a^(-5)+a^(-4)+a^(-3)+a^(-3)+a^(-3)+1+a^(8)+a^(10))/(8)`
`ge(a^(-5)xxa^(-4)xxa^(-3)xxa^(-3)xxa^(-3)xx1xxa^(8)xxa^(10))^(1//8)`
`implies" "(a^(-5)+a^(-4)+3a^(-3)+1+a^(8)+a^(10))/(8)ge1`
`implies" "a^(-5)+a^(-4)+3a^(-3)+1+a^(8)+a^(10)ge8`
Hence, the minimum value of `a^(-5)+a^(-4)+3a^(-3)+1+a^(8)+a^(10)` is 8.