SOLUTION: if a,b,c in ap nd x,y,z in gp prove that x^b y^c z^a=x^c y^a z^b

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Question 1012113: if a,b,c in ap nd x,y,z in gp prove that x^b y^c z^a=x^c y^a z^b
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Since a, b, and c are in an arithmetic progression, we can write them as
a, a + d, and a + 2d.
Since x, y, and z are in geometric progression , we can write them as
x, xr and xr^2.
Thus we can substitute into
x^b y^c z^a = x^c y^a z^b
and get

which yields

Now collect like bases and get
x%5E%283a%2B3d%29%2Ar%5E%283a%2B2d%29+=+x%5E%283a%2B3d%29%2Ar%5E%283a%2B2d%29
and we're done...