The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. The square of their sum is:

Question: The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. The square of their sum is:

Solution:
Let the numbers be a, b and c

Then,
a² + b² + c² = 138
(ab + bc + ca) = 131

Now,
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
⇒ (a + b + c)² = 138 + 2 × 131
∴ (a + b + c)² = 400