Question

${a}^{2} + {b}^{2} + {c}^{2} = 21$
$a + b - c = 7$
$ab - bc - ac =$
?​

Answer 1

(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

Answer 2

a² + b² + c² = 21

a + b - c = 7

(a + b - c)² = 7²

[(a + b) - c]² = 49

(a + b)² - 2 * (a + b) * c + c² = 49

a² + 2ab + b² - 2ac - 2bc + c² = 49

(a² + b² + c²) + 2ab - 2bc - 2ac = 49

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

2(ab - bc - ac) = 28

ab - bc - ac = 14