Question

If (x + a)(x + b)(x + c) = x³ + 14x² + 59x + 70, find the value of a² + b² + c² 

Answer 1

(x + a)(x + b)(x + c) = x³ + 14x² + 59x + 70

x³ + (a + b + c)x² + (ab + bc + ac)x + abc = x³ + 14x² + 59x + 70

a + b + c = 14, ab + bc + ac = 59, abc = 70

a² + b² + c² = (a + b + c)² – 2(ab + bc + ac)

= (14)² – 2(59)

= 196 – 118

= 78