Discussion
If the sum of two numbers is 22 and the sum of their squares is 404, then the product of the numbers is:
Answer: A
Expand the square of the sum.
\[ (a+b)^{2} = a^{2} + b^{2} + 2ab \]
\[ 22^{2} = 404 + 2ab \quad\Longrightarrow\quad 484 - 404 = 2ab \]
\[ ab = 40 \]
The two numbers turn out to be 2 and 20.
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