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Sagot :
a) The product of the three absolute values is equal to 72.
b) There are four combinations to obtain a positive number by multiplication:
- 2, 4, 9
- - 2, - 4, 9
- - 2, 4, - 9
- 2, - 4, - 9
How to obtain the product of three numbers as a positive number
According to algebra, absolute values (i.e. |x|) are expressions defined by the following formula:
- |x| = x, for x ≥ 0.
- |x| = - x, for x < 0.
a) In this statement we notice that 2 can be generated both from 2 and - 2, 4 from 4 and - 4 and 9 from 9 and - 9. Then, the product of the three numbers is presented below:
|x₁| · |x₂| · |x₃| = 2 · 4 · 9 = 72
The product of the three absolute values is equal to 72.
b) According to sign laws, there are two forms of obtaining a positive number from three numbers:
- Three positive numbers.
- Two negative numbers and a positive number.
Based on all these facts, we can conclude the existence of four sign scenarios related to the three absolute numbers:
- x₁ = 2, x₂ = 4, x₃ = 9
- x₁ = - 2, x₂ = - 4, x₃ = 9
- x₁ = - 2, x₂ = 4, x₃ = - 9
- x₁ = 2, x₂ = - 4, x₃ = - 9
To learn more on absolute values: https://brainly.com/question/1301718
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