[tex] a^2 + b^2 + c^2 = 21[/tex][tex] a + b

a + b + c = 21

a + b - c = 7

(a + b - c) = 7

[(a + b) - c] = 49

(a + b) - 2 * (a + b) * c + c = 49

a + 2ab + b - 2ac - 2bc + c = 49

(a + b + c) + 2ab - 2bc - 2ac = 49

21 + 2(ab - bc - ac) = 49

2(ab - bc - ac) = 28

ab - bc - ac = 14

(a+b-c)^2 = a*a + b*b + c*c + 2ab -2ac -2bc

2ab -2ac -2bc = (a+b-c)^2 - a*a + b*b + c*c = 49 - 21 = 28

ab -ac -bc = 28/2 = 14