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

If a,b,c are in A.P.,prove that - a^3-8b^3+c^3+6abc=0

If a,b,c,d are in G.P. then 1/(a^3+b^3),1/(b^3+c^3),1/(c^3+d^3) are also in G.P.

If a + b + c = 0 , then prove that (a^2+b^2+c^2)/(a^3+b^3+c^3)+2/3(1/a+1/b+1/c)=0

If a + 2b = 4c , then prove that a^3+8b^3-64c^3+24abc=0

If a,b,c are positive unequal real numbers then prove that a^2+b^2+c^2gtab+bc+ca . Hence prove that a^3+b^3+c^3gt3abc