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`.

If x,y,z are in G.P and a^(x)=b^(y)=c^(z), then

If a^x=b^y=c^z and a,b,c are in G.P. show that 1/x,1/y,1/z are in A.P.

If x,1,z are in A.P. x,2,z are in G.P., show thast 1/x,1/4,1/z are in A.P.

If a, b, c are in A.P. and x, y, z are in G.P., then prove that : x^(b-c).y^(c-a).z^(a-b)=1

If x,y,z are in A.P.;ax,by,cz are in GP and (1)/(a),(1)/(b),(1)/(c) are in A.P., then (x)/(z)+(z)/(x) is equal to