SOLUTION: if a,b,c are in an arithmetic progression and x,y,z are in a geometric progression prove that x^b*y^c*z^a = x^c*y^a*z^b

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Question 1014418: if a,b,c are in an arithmetic progression and x,y,z are in a geometric progression prove that x^b*y^c*z^a = x^c*y^a*z^b
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
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if a,b,c are in an arithmetic progression and x,y,z are in a geometric progression prove that x^b*y^c*z^a = x^c*y^a*z^b
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Since a, b, c are in an arithmetic progression, we have 
   a = b - d, c = b + d.

Since x, y, z are in an geometric progression, we have 
   x = y*r^(-1), z = y*r.

Now,   x^b*y^c*z^a =  .  .  =  .  = ..

Next,  x^c*y^a*z^b =  .  .  =  .  = ..

Right sides are the same.
So are left sides.

Proved.


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