Answer:
7 and 12
Solution:
Let x be the greater number and y be the lesser number
[tex]x + y = 19[/tex]
[tex]y = -x +19[/tex]
[tex]x(x-y) = 60[/tex]
Substitute x for y
[tex]x(x-(-x+19)) = 60[/tex]
[tex]2x^2 + 19x = 60[/tex]
Subtract 60 to both sides
[tex]2x^2 + 19x - 60[/tex]
Solve this using quadratic formula where a = 2, b = 19 and c = -60
[tex]x = \frac{-b±\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x = \frac{-19±\sqrt{-19^2-4(2)(-60)} }{2(2)}[/tex]
[tex]x = \frac{-19±\sqrt{841} }{4}[/tex]
[tex]x = 12[/tex]
We will ignore 2.5 because 2.5 doesnt comply the sum of 19
Since we already found x, we can now find y
x + y = 19
12 + y = 19
y = 7
Therefore x = 12 and y = 7
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