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Two positive numbers have a difference of 4 and a product of 96. What are the numbers

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MathG33kidn
I used guess and check for this one, it would be 8 and 12, they both have a difference of 4 and a product of 96.
Konrad509idn
[tex]x-y=4\\ xy=96\\\\ x=4+y\\ xy=96\\\\ (4+y)y=96\\ 4y+y^2=96\\ y^2+4y-96=0\\ y^2+4y+4-100=0\\ (y+2)^2=100\\ y+2=10 \vee y+2=-10\\ y=8 \vee y=-12\\ x=4+8\\ x=12\\\\ 8 \hbox{ and } 12[/tex]
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