Question

solve this problem: click on it to maximize it

Answer 1

let x be the A.M of a & b
then x= (a+b) /2 ------(1)
also by given data ,
a^(p+1) + b^(p+1)
------------------------- is also A.M of a & b .
a^p +b^p
if and only if it is equal to (a+b)/2.

put p=0 ,. a^(0+1) +b^(0+1). a+b
-------------------------. = ------
a^0 +b^0. 1+1


= (a+b) /2
hence if it so p=0
hence proved
hope it is useful to u!