If one Arithmetic Mean (A) and two Geometric Means (p,q) are inserted between two given numbers, show that
Call the original numbers x and y. There arithmetic mean is . Strictly speaking, two numbers have only one geometric mean but I think that you mean that x, p, q, y form a geometric progression. That would mean that p= xr, [tex]q= xr^2[tex] and . Dividing y by x, so that and so and .
Put those into and see if you get 2A= x+ y.