If the sum of the squares of three numbers is 138, and the sum of the products of these numbers taken two at a time is 131, what is the sum of the three numbers?

Explanation

Let the three numbers be x, y, and z. Given that x² + y² + z² = 138 and xy + yz + zx = 131. Using the identity (x + y + z)² = x² + y² + z² + 2(xy + yz + zx), we get (x + y + z)² = 138 + 2(131) = 138 + 262 = 400. Therefore, x + y + z = √400 = 20.