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vlada-n [284]
4 years ago
6

The difference between two numbers is 2 and their product is 224. What are the numbers?

Mathematics
1 answer:
Sati [7]4 years ago
4 0

Let x,y be the two numbers. We have two pieces of information:

x-y=2 (the difference between the two numbers is 2)

xy=224 (their product is 224)

From the first equation, we can deduce x=y+2

If we plug this expression in the second equation, we have

xy = (y+2)y = 224 \iff y^2+2y-224 =0

If you solve this equation with the usual quadratic formula you get the solutions

y=-16,\quad y=14

So, you have the following couple of solutions, recalling that x is 2 more than y:

\begin{cases} x = -14\\y=-16\end{cases},\quad\begin{cases} x = 16\\y=14\end{cases}

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