If a,b,c are in G.P then show that `(a+2b+2c)(a-2b+2c)=a^2+4c^2`

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

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

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

If a,b,c are in G.P then show that a^2b^2c^2(1/a^3+1/b^3+1/c^3)=a^3+b^3+c^3 .

If a,b,c are in G.P., show that 1/(a+b),1/(2b),1/(b+c) are in A.P.

If a, b, c are in A.P. and also in GP., show that a = b = c.

If a, b, c are in A.P. then show that the terms given below are also in A.P. (b+c)^2-a^2,(c+a)^2-b^2,(a+b)^2-c^2 .

If a, b, c are in A.P. then show that the terms given below are also in A.P. a^2(b+c),b^2(c+a),c^2(a+b),{ab+bc+cane0} .

If a, b, c are in A.P. and a, b, c + 1 are in G.P. then prove that 4a=(a-c)^2 .

If a+b+c=0 , then prove that (a^2+b^2+c^2)^2=4 (a^2b^2+b^2c^2+c^2a^2)