SOLUTION: two positive integers with a difference of six. if the smaller is added to the square of the larger the sum is 84. what are the two integers?

Question 313304: two positive integers with a difference of six. if the smaller is added to the square of the larger the sum is 84. what are the two integers?
Answer by moshiz08(60) (Show Source): You can put this solution on YOUR website!
Let's call the bigger integer and the smaller integer .
The difference is six. In an equation, this means . Another way to write this is: .
if the smaller is added to the square of the larger the sum is 84: this means .
Let's substitute our expression for into this equation. Then we have

so subtracting 84 from both sides gives: .
Now we can factor: . Therefore, there are two solutions: or . Since the integer must be positive, we know our answer is .
Now we can find from the fact that the difference is 6: implies that .
So we have the solution x = 9, y = 3.
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