The sum of the squares of two nonnegative numbers is 327. The product of the two numbers is \(85\). What is the sum of the two numbers?
Let a and b be the two numbers.
\(\begin{cases}a^2 + b^2 = 327\\ab = 85\end{cases}\)
We want to find a + b, but we only have quadratic terms in our equations, so we consider (a + b)^2 instead.
\((a + b)^2 = a^2 +b^2 + 2ab = 327 + 2(85) = 497\)
Suppose x = a + b. Then x^2 = 497. Can you take it from here?
Hint: The value of x is NOT negative since a and b are nonnegative numbers.