If `(a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx)/(c-dx)(x!=0),`then show that a, b, c and d are in G.P.

If (a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx)/(c-dx)(x!=0) , then show that a ,\ b ,\ c\ a n d\ d are in G.P.

If (a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx)/(c-dx)(x!=0) , then show that a ,\ b ,\ c\ a n d\ d are in G.P.

If a,b,c,d………are in G.P., then show that (a+b)^2, (b+c)^2, (c+d)^2 are in G.P.

If a,b,c,d………are in G.P., then show that (a-b)^2, (b-c)^2, (c-d)^2 are in G.P.

(x^a/x^b)^(a+b).(x^b/x^c)^(b+c).(x^c/x^a)^(c+a)

If (x^(4))/((x-a)(x-b)(x-c))= P(x)+(A)/(x-a)+(B)/(x-b)+(C)/(x-c) then P(x)=

If a, b are the roots of equation x^(2)-3x + p =0 and c, d are the roots of x^(2) - 12x + q = 0 and a, b, c, d are in G.P., then prove that : p : q =1 : 16

If x, a, b, c are real and (x-a+b)^(2)+(x-b+c)^(2)=0 , then a, b, c are in

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 the determinant |(a ,b,2aalpha+3b),(b, c,2balpha+3c),(2aalpha+3b,2balpha+3c,0)|=0 then (a) a , b , c are in H.P. (b) alpha is root of 4a x^2+12 b x+9c=0 or(c) a , b , c are in G.P. (d) a , b , c , are in G.P. only a , b ,c are in A.P.