Respuesta :
ummm if its multiply then its 1 and 6. is its addition then its 1 and 5 or 6 and 0. if its divide it would be 6 and 1. is its subtraction then it would be 7 and 1 or 6 and 0
Given that the difference between two numbers is 6, and their product is as small as possible, using the concept of vertex of parabola, the numbers are -3 and 3.
What is vertex of a parabola?
The vertex of a parabola is the point where the parabola crosses its axis of symmetry.
To find the vertex of a parabola that is in vertex form y = a (x - h)²+ k
Let one number be x.
Another number be 6 greater than x. Let it be x + 6.
[tex]P = x(x + 6) = x^{2} + 6x\\[/tex]
This can be rewritten in the vertex form.
In a parabola of the form y = a (x - h)²+ k, if a > 0, the parabola opens up, if a < 0, the parabola opens down.
Since, in P = x² + 6x, a = 1 > 0, the parabola opens up. Therefore, the vertex of the parabola is the minimum point. Therefore, it is used here.
[tex]P = x^{2} + 6x \\\\P = x^{2} + 2(3)(x) + 3^{2} -3^{2} \\\\P = (x+3)^{2} -9\\ \\[/tex]
Vertex : (-3,-9)
x = -3
x + 6 = -3 + 6 = 3
The pair of two numbers are -3 and 3.
Learn more about vertex of the parabola here
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