SOLUTION: The sum of two integers is 15. Their product is 9 more than the difference of their squares. Find the integers.

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Question 180579: The sum of two integers is 15. Their product is 9 more than the difference of their squares. Find the integers.
Answer by HyperBrain(694) About Me  (Show Source):
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Let x,y=two integers


x+y=15 The sum of two integers is 15.

xy=x2-y2+9 Their product is 9 more than the difference of their squares.

x2-y2=(x+y)(x-y)=15(x-y)=15x-15y
So,
xy=15x-15y+9
Since x+y=15, y=15-x so,
x(15-x)=15x-15(15-x)+9
15x-x2=15(x-15+x)+9=15(2x-15)+9=30x-225+9=30x-216
x2+15x-216=0
(x+24)(x-9)=0
So x=-24 or 9
If x=-24, y=15-(-24)=15+24=37
if x=9 y=15-9=6
Therefore, there are two solutions: the integers are either -24 and 37, or 6 and 9.
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