The sum of squares of three numbers is 138 and the sum of their products taken…

Step-by-Step Solution

To find the sum of three numbers, we can use the algebraic identity for the square of a trinomial.

1. Define the variables and given values:

   • Let the three numbers be x, y, and z.

   • Sum of squares: x^2 + y^2 + z^2 = 138.

   • Sum of products taken two at a time: xy + yz + zx = 131.

2. Apply the algebraic identity: The identity for the square of a sum is: (x + y + z)^2 = x^2 + y^2 + z^2 + 2(xy + yz + zx)

3. Substitute the known values:

   • (x + y + z)^2 = 138 + 2(131)

   • (x + y + z)^2 = 138 + 262

   • (x + y + z)^2 = 400

4. Solve for the sum (x + y + z):

   • x + y + z = sqrt(400)

   • x + y + z = 20