The sum of two integers is 26. the sum of the squares of the two integers is 340. what is the product of the two numbers?

Lets say that the two unknown integers are  and .

We know the following things about and :




And, we want to find .

To solve this, we'll use the expansion of the squared of the sum of any two inegers; this is expressed as:



So, given what we know about the unknown integers, the previous can be written as:



We can easily solve for :



The answer is 168.

Another approach to solve the problem is, from the two starting equations, compute the values of  and , which are 12 and 14, and directly compute their product; however, the approach described is more elegant. 

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