If a + b + c = 0 and a² + b² + c² = 16, find the value of ab + bc + ca.

a + b + c = 0 and a² + b² + c² = 16 (given)

Choose a + b + c = 0

Squaring both sides,

(a + b + c)² = 0

a² + b² + c² + 2(ab + bc + ca) = 0

16 + 2(ab + bc + c) = 0

2(ab + bc + ca) = -16

ab + bc + ca = -16/2 = -8

or ab + bc + ca = -8