If a² + b² + c² = 125 and ab + bc + ca = 50, find a + b + c.

We know that,

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

Substituting values we get,

⇒ (a + b + c)² = 125 + 2(50) = 125 + 100 = 225.

$\therefore (a + b + c) = \sqrt{225} = \pm 15.$

Hence, (a + b + c) = ± 15.