Question

If a, b, c are in AP and x, y, z are in GP then prove that the value of x^{b - c} . y^{c - a} . z ^{a - b} is 1.

Answer 1

To prove: x^{b - c} . y^{c - a} . z^{a - b} = 1….(i) 

It is given that a,b,c are in A.P. 

⇒ 2b = a + c…(ii) 

And x,y,z, are in G.P. 

⇒ y² = xz 

⇒ x = y² /z 

Substitute this value of x in equation (i),we get 

L.H.S =

Hence, proved that . If a, b, c are in AP and x, y, z are in GP then x^{b - c} . y^{c - a} . z^{a - b}= 1