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.

Question

Philoid · Accepted Answer

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 =

⇒

⇒ y⁰.z⁰…(Using equation (i))

= 1 = R.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