The sum of squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find their sum.

Question: The sum of squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find their sum.Solution:Let the three numbers be x, y and z.Sum of squares of three numbers is 138 and sum of their products taken two at a time is 131Therefore,x2 + y2 + z2 = 138xy + yz + zx = 131(x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)(x + y + z )2 = 138 + 2(131)(x + y + z )2 = 400Hence, (x + y + z) = 20