The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum isSelect one:a. 40b. 30c. None of thesed. 20

To solve this problem, let's assume the three numbers as a, b, and c.

Step 1: We are given that the sum of the squares of the three numbers is 138. So, we can write the equation as: a^2 + b^2 + c^2 = 138

Step 2: We are also given that the sum of their products taken two at a time is 131. This means: ab + ac + bc = 131

Step 3: We need to find the sum of the three numbers, which is a + b + c.

To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method.

Step 4: From equation 2, we can express one variable in terms of the other two variables. Let's solve for a in terms of b and c: a = (131 - bc)/(b + c)

Step 5: Substitute the value of a in equation 1: [(131 - bc)/(b + c)]^2 + b^2 + c^2 = 138

Step 6: Simplify the equation and solve for b and c. This will give us the values of b and c.

Step 7: Once we have the values of b and c, substitute them back into equation 2 to find the value of a.

Step 8: Finally, calculate the sum of the three numbers by adding a, b, and c.

Step 9: Compare the calculated sum with the given options (a, b, c, or none of these) to find the correct answer.

Unfortunately, without solving the equations, we cannot determine the exact value of the sum of the three numbers. Therefore, the correct answer is option c. None of these.