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About LinkBacksIf one Arithmetic Mean (A) and two Geometric Means (p,q) are inserted between two given numbers, show that
/q}+{(q^2)/p}=2A)
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 intoand see if you get 2A= x+ y.
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