If a + b + c = 7 then find the range of a b + b c + a c

a + b + c = 7 (a + b + c)^2 = 49a^2+ b^2 +c^2 + 2( ab+bc+ca) =49ab+bc+ca = {49 -( a^2+ b^2+ c^2 )}/2Here, a^2+ b^2 + c^2 is never negative so range is(-∞, 49/2)