The pair two numbers whose difference is 14 and the product is as small as possible (i.e. -49) are (-7,7)
In mathematical concepts, word problems involve a crucial understanding of the problem and knowing which mathematical method and arithmetic operations are best suited to solving the problem.
If we assume that the smaller number should be = a and the larger number = a + 14.
Thus, their product (X) can be expressed as:
= a(a+14)
= a² + 14a
The smallest possible value implies the minimum value, i.e.
[tex]\mathbf{\dfrac{dX}{da} = 2a + 14}[/tex]
Thus,
2a + 14 = 0
a = - 14/2
a = -7
Therefore, we can conclude that the pair of two numbers whose difference is 14 and the product is as small as possible (i.e. -49) is (-7,7).
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