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Sati [7]
2 years ago
6

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?

Mathematics
1 answer:
Phoenix [80]2 years ago
5 0
Lets say that the two unknown integers are n and m.

We know the following things about n and m:

n+m=26
n^2+m^2=340

And, we want to find nm.

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

(n+m)^2=n^2+2nm+m^2

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

(26)^2=340+2nm

We can easily solve for nm:

nm= \frac{(26)^2-340}{2}= \frac{676-340}{2}= \frac{336}{2}=168

The answer is 168.

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