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?

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call the bigger integer x and the smaller integer y.
The difference is six. In an equation, this means +x+-+y+=+6+. Another way to write this is: +y+=+x+-+6+.
if the smaller y is added to the square of the larger x%5E2 the sum is 84: this means +y+%2B+x%5E2+=+84+.
Let's substitute our expression for +y+ into this equation. Then we have
+y+%2B+x%5E2+=+%28+x+-+6%29+%2B+x%5E2+=+84+
so subtracting 84 from both sides gives: +x%5E2+%2B+x+-+90+=+0+.
Now we can factor: +x%5E2+%2B+x+-+90+=+%28x+-+9%29+%2A+%28x+%2B+10%29+=+0. Therefore, there are two solutions: +x+=+9 or x+=+-10. Since the integer must be positive, we know our answer is +x+=+9.
Now we can find y from the fact that the difference is 6: +x+-+y+=+9+-+y+=+6 implies that y+=+3.
So we have the solution x = 9, y = 3.