Answer: ab + bc + ac = 155
Explanation:
Given: a² + b² + c² = 90 and a + b + c = 20
Square the second equation, subtract it from the first equation, then simplify.
Square the second equation:
(a + b + c)² = 20²
a² + b² + c² + 2ab + 2bc + 2ac = 400
Subtract the equations:
a² + b² + c² + 2ab + 2bc + 2ac = 400
- (a² + b² + c² = 90)
2ab + 2bc + 2ac = 310
Simplify:
2(ab + bc + ac) = 310
÷2 ÷2
ab + bc + ac = 155