Hey there!
Let x equal the smaller positive number and let y equal the greater number.
We can represent the product of the two numbers equaling 112 with this equation:
xy=112
We can represent the larger number being greater than the smaller number by 6 with this equation:
y=x+6
Because you know that the value of y is equal to x+6, you can substitute x=6 for y in the first equation:
y=x+6
xy=112
x(x+6)=112
Now, simplify and set your equation to 0 so the equation can be solved as a quadratic:
x(x+6)=112
[tex] x^{2} [/tex]+6x=112
[tex] x^{2} [/tex]+6x-112=0
Use the quadratic formula to solve for the values of x:
[tex] \frac{-6+- \sqrt{ 6^{2} -4(-112)(1)} }{2} [/tex]
[tex] \frac{-6+- \sqrt{36+448} }{2} [/tex]
[tex] \frac{-6+- \sqrt{484} }{2} [/tex]
[tex] \frac{-6+-22}{2} [/tex]
x=8 or -14
Because you want a positive solution, you would use x=8 as one of your final solutions.
Now, you need to find the other number.
To do this, plug x=8 into y=x+6.
y=8+6
y=14
Therefore, your final answers would be 8 and 14.
Hope this helps!
