Question

if x+y+z=a and the minimum value of a/x +a/y + a/z is 81^n, then the value of n is
a) 1/2
b) 1
c) 1/4
d)2

Answer 1

a/x+a/y+a/z=(x+y+z) (1/x+1 /y+1 /z)
=3+x/y+y/x+y/z+z/y+z/x+x/z greater than or equal to 9
X/Y+Y/X always greater than or equal to 2
The minimum value is 9
Square root of 81=9
Therefore n=1/2