Question

a, b, c are in A.P and x, y, z are in G.P.
Prove that x^b-c, y^c-a , z^a-b = 1​

Answer 1

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Answer 2

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Answer

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Given a,b,c are in A.P

⟹2b=a+c

And also x,y,z are in G.P

⟹y=xz

LHS=xb−c.yc−a.za−b=xb−c.za−b.(xz)c−a=xb−c.za−b.x2c−a.z2c−a=x22b−(a+c)z22b−(a+c)=x0.z0=1