If a, b, c and d are in G.P. show that `(a^2+ b^2+ c^2) (b^2 + c^2 + d^2)= ( ab + bc + cd)^2` .

If a,b,c, d are in G.P., show that : a^(2)+b^(2), b^(2)+ c^(2) and c^(2)+d^(2) are also in G.P.

If a,b,c, d are in G.P., show that : a+b,b+ c and c+d are also in G.P.

If (a + ib) (c + id) (e + if) (g + ih) = A + iB , then show that (a^2 + b^2) (c^2 + d^2) (e^2 +f^2) (g^2+ h^2) = A^2 + B^2

If a, b, c are in A.P., prove that : (b+c)^2-a^2, (c+a)^2-b^2, (a+b)^2-c^2 are also in A.P.

If a^2 (b+c),b^2(c+a) , c^2(a+b) are in A.P., show that : either a, b, c are in A.P. or ab + bc + ca =0.

If (a+ib)/(c+id)=x + iy , show that : x^2+y^2= (a^2+b^2)/(c^2 +d^2) .

If a,b,c are in AP, than show that a^(2)(b+c)+b^(2)(c+a)+c^(2)(a+b)=(2)/(9)(a+b+c)^(3) .

If a, b,c are in G.P., prove that the following are also in G.P. : a^(2),b^(2),c^(2) .

If a,b,c,d ,e are +ve real numbers such that a+b+c+d+e=8 and a^2 + b^2 +c^2 + d^2 +e^2 = 16 , then the range of 'e' is