If a be one A.M and `G_1` and `G_2` be then geometric means between b and c then `G_1^3+G_2^3=`

Explanation

It is given that a is the A.M. of b and c. So,
`a=(b+c)/2` or b+c=2a
Since `G_(1)` and `G_(2)` are two geometric means between b and c, so b,`G_(1),G_(2)`,c is a G.P. with common ratio `r=(c//b)^(1//3)`. Therefore,
`G_(1)=b(c/b)^(1/3),G_(2)=b(c/b)^(2/3)`
`rArrG_(1)^(3)+G_(2)^(3)=b^(2)c+bc^(2)`
=bc(b+c)
=2abc [Using (1)]