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# Algebra

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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?

May 14, 2022

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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.

May 14, 2022