Question

if A1 and A2 are arithmetic means between any two real numbers a and b and G1 and G2 are geometric means between a and b express A1+A2/G1G2 in terms of a and b.

Answer 1

AP: a, a+(b-a)/3, a+(2(b-a)/3, b
A1 = (2a+b)/3
A2 = (a+2b)/3
GP: a, a∛(b/a), a∛(b^2/a^2), b
G1 = ∛(a^2b)
G2 = ∛(ab^2)
A1+A2 = a+b
G1*G2 = ab

Answer 2

frist identify a given terms. then done in form of above explinations.