If a+bxa−bx = b+cxb−cx = c+dxc−dx(x ≠ 0), then a, b, c, d are in:
A.P.
G.P.
H.P.
A.G.P
USING COMPONENDO AND DIVIDENDO RULE, we have abx = bcx = cdx
⇒ ac = b2, bd = c2
So, a, b, c, d are in G.P.
If a+bxa−bx=b+cxb−cx=c+dxc−dx(x≠0), then show that a, b, c and d are in G.P.
If a+bxa−bx=b+cxb−cx=c+dxc−dx (x≠0), then show that a, b, c and d are in G.P.