Answer:
Numbers: 6 and -2
Step-by-step explanation:
Equations
This question can be solved by inspection. It's just a matter of factoring 12 into two factors that sum 4. Both numbers must be of different signs and they are 6 and -2. Their sum is indeed 6-2=4 and their product is 6*(-2)=-12.
However, we'll solve it by the use of equations. Let's call x and y to the numbers. They must comply:
[tex]x+y=4\qquad\qquad [1][/tex]
[tex]x.y=-12\qquad\qquad [2][/tex]
Solving [1] for y:
[tex]y=4-x[/tex]
Substituting in [2]
[tex]x(4-x)=-12[/tex]
Operating:
[tex]4x-x^2=-12[/tex]
Rearranging:
[tex]x^2-4x-12=0[/tex]
Solving with the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
With a=1, b=-4, c=-12:
[tex]\displaystyle x=\frac{-(-4)\pm \sqrt{(-4)^2-4(1)(-12)}}{2(1)}[/tex]
[tex]\displaystyle x=\frac{4\pm \sqrt{16+48}}{2}[/tex]
[tex]\displaystyle x=\frac{4\pm 8}{2}[/tex]
The solutions are:
[tex]\displaystyle x=\frac{4+ 8}{2}=6[/tex]
[tex]\displaystyle x=\frac{4- 8}{2}=-2[/tex]
This confirms the preliminary results.
Numbers: 6 and -2
