If a, b, c are positive, prove that (a + b + c) (ab + bc + ca) `ge` 9abc.

Prove (a + b + c) (ab + bc + ca) > 9abc

If a, b, c are all positive, prove that 6abc le bc(b + c) + ca(c + a) + ab(a + b)

If (a-b), (b-c), (c-a) are in GP then prove that (a+b+c)^2 =3(ab+bc+ca)..

If a, b, c are positive number satisfying 4ab + 6bc + 8ca = 9, then find the greatest value of (abc).

If a, b, c are in H.P., prove that, (1)/(bc), (1)/(ca), (1)/(ab) are in H.P.

If a, b, c one positive numbers satisfying 4ab + 6bc + 8ca = 9 find the greatest value of (abc).

If the lengths of the sides vec(BC), vec(CA) and vec(AB) of the triangle ABC be a:b:c respectively and the lengths of perpendicular from the circumcenter upon vec(BC), vec(CA) and vec(AB) be x, y, z respectively, then prove that, a/x + b/y + c/z = (abc)/(4xyz) .

If a, b, c are in A.P., show that, (bc)/(a(b+c)), (ca)/(b(c+a)) and (ab)/(c(a+b)) are in H.P.

If a, b and c are three positive real numbers, show that a^2 + b^2 + c^2 ge ab + bc + ca

If a : b = b : c , then prove that (abc(a+b+c)^(3))/((ab+bc+ca)^(3)) = 1