If `x^(2),y^(2),z^(2)` are in AP, then `y+z,z+x,x+y` are in

If x,y,z, are in A.P. and x^(2),y^(2),z^(2) are in H.P., then which of the following is correct ?

If x,y,z, are in A.P. and x^(2),y^(2),z^(2) are in H.P., then which of the following is correct ?

If reciprocals of (y-x),2(y-a),(y-z) are in A.P then prove that x-a, y-a, z-a are in G.P

If x,y,z are in AP,then show that the following are also in AP: (y+z)^(2)-x^(2),(z+x)^(2)-y^(2),(x+y)^(2)-z^(2)

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

If reciprocals of (y-x),2(y-a), (y-z) are in A.P., prove that x-a,y-a,z-a are in G.P.

If reciprocals of (y-x),2(y-a), (y-z) are in A.P., prove that x-a,y-a,z-a are in G.P.

a, b, x are in AP, a, b, y are in GP and a, b, z are in HP, then prove that 4z(x-y)(y-z)=y(x-z)^2 .

If Delta = abs{:(x+y+z^(2) , x^(2) + y+ z, x+y^(2) + z),(z^2, x^2, y^2),(x+y,y+z,x+z):} , (where ( x ne y ne z) x, y, z in R- {0} ) then Delta= ........