A1 IS THE ARITHMETIC MEAN BETWEEN `a` and `b`. G1 and G2 ARE TWO GEOMETRIC MEANS BETWEEN `a` and `b`. Value of G1³ + G2³ /G1*G2*A1

A1 = a+b/2 --- (1)
Now, a G1 G2 b are in GP so
b = ar³ or r = (b/a)^1/3
So G1 = ar = a(b/a)^1/3 and G2 = ar² = a(b/a)^2/3 ----- (2)
Now use the values of A1, G1 and G2 from the above equations and get the value.

Thanks, Vj