Answer:

The two numbers are ±16 and ±12

Step-by-step explanation:

Given that the ratio of the two numbers is [tex]4:3[/tex], we can express the two numbers as [tex]4x[/tex] and [tex]3x[/tex] for some constant [tex]x[/tex].

Use these variables to create an equation from "the product of two numbers is 192":

[tex](4x)(3x)=192[/tex]

[tex]12x^2=192[/tex]

[tex]\displaystyle \frac{12x^2}{12} =\frac{192}{12}[/tex]

[tex]x^2=16[/tex]

[tex]x=\pm \sqrt{16}[/tex]

[tex]x=\pm 4[/tex]

Therefore, the two numbers are [tex]4x=4(\pm 4)=\pm 16[/tex] and [tex]3x=3(\pm 4)=\pm 12[/tex].