If a + b - c = -5 and ab - bc - ac = 10, then find the value of $a^2 + b^2 + c^2 $
Answer & explanation
Correct answer: option 2
a + b - c = 5
ab - bc - ac = 10
(a + b - c)2 = a2 + b2 + c2 + 2ab - 2bc - 2ac
= (5)2 = a2 + b2 + c2 + 2(ab - bc - ac)
= 25 = a2 + b2 + c2 + 2 × 10
= a2 + b2 + c2 = 25 - 20
= a2 + b2 + c2 = 5