Answer:
B. 14 and 10
Solution:
x + y = 24
x(y) = 140
Since x + y = 24, thus y = 24 - x
Substitute x for y
x(24-x) = 140
Expand the expression
24x - x^2 = 140
Subtract 140 to both sides.
24x - x^2 - 140
Rearrange the equation to the form of [tex]ax^2 + bx + c[/tex] which can be solved using quadratic formula [tex]x = \frac{-b±\sqrt{b^2-4ac} }{2a}[/tex]
[tex]-x^2 + 24x - 140[/tex]
Thus, a = -1, b = 24 and c = -140
Substitute the value
[tex]x=\frac{-24±\sqrt{24^2-4(-1)(-140)} }{2(-1)}[/tex]
[tex]x=\frac{-24±\sqrt{576-560} }{-2}[/tex]
[tex]x = 10[/tex] or [tex]x = 14[/tex]
Therefore the integers are 10 and 14
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