If `5x-y,2x+y,x+2y`are in "A.P" and `(x-1)^(2),xy+1,(y+1)^(2)`are in G.P`(x!=0)` then `x+y=`

The complex numbrs x and y such that x,x+2y,2x+y are n A.P. and (y+1)^2, xy+5, (x+1)^2 are in G.P. are (A) x=3, y=1 (B) x=-1+2sqrt(2)i, y=1/3 (-1+2sqrt(2)i) (C) x=sqrt(2)+i, y=3sqrt(5)-sqrt(2)i (D) x=-1(1+2sqrt(2)i), y= - 1/3 (1+2sqrt(2)i)

If reciprocals of (x+y)/2,y, (y+z)/2 are in A.P., show that x,y,z are in G.P.

If tan^(-1)x,tan^(-1)y,tan^(-1)z are in A.P the (2y)/(1-y^(2))=

If distinct numbers x,y,z are in G.P. and 1/(x+a),1/(y+a),1/(z+a) are in A.P., prove that a=y .

Given that x+y+z =15 when a,x,y,z,b are in A.P and 1/x+1/y+1/z=5/3 when a,x,y,z,b are in H.P .Then