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

If a, b, c are in A.P. then show that 3^(a), 3^(b), 3^(c) are in G.P.

If a ,b ,c ,da n dp are distinct real numbers such that (a^2+b^2+c^2)p^2-2(a b+b c+c d)p+(b^2+c^2+d^2)lt=0, then prove that a ,b ,c , d are in G.P.

Evaluate lim_(xtooo) (1+(1)/(a+bx))^(c+dx) , where a, b, c, and d are positive.

If ax^(2)+ bx +c and bx ^(2) + ax + c have a common factor x +1 then show that c=0 and a =b.

If |{:(a,b,a alpha+b),(b,c,b alpha+c),(a alpha +b,b alpha+c,0):}|=0 Prove that a,b,c are in G.P. or alpha is a root of ax^2 + 2bx + c=0

Prove that =|a c c-a +b c b b-c b+c a-b b-c 0 a-c x y z 1+x+y|=0 implies that a ,b ,c are in A.P. or a ,c ,b are in G.P.

If (x ^(2) -1) is a factor of ax ^(4) + bx ^(3) + cx ^(2) + dx +e, then show that a + c +e =b +d=0

If l n(a+c),l n(a-c)a n dl n(a-2b+c) are in A.P., then (a) a ,b ,c are in A.P. (b) a^2,b^2, c^2, are in A.P. (c) a ,b ,c are in G.P. d. (d) a ,b ,c are in H.P.

If |(a,b,aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c,0)|=0, prove that a,b,c, are in G.P. or alpha is a root of ax^(2)+ 2bx+c=0

"If " int x e^(x) cosx dx=ae^(x)(b(1-x)sinx+cx cosx)+d, then