Answer:
12.5 and 13
Step-by-step explanation:
Let the numbers are x and y,
So, their average = [tex]\frac{x+y}{2}[/tex]
And, their product = xy
According to the question,
[tex]\frac{x+y}{2}=12.75[/tex]
[tex]x+y = 25.5-----(1)[/tex]
Also,
xy = 162.5
[tex]\implies x =\frac{162.5}{y}----(2)[/tex],
From equation (1) and (2),
[tex]\frac{162.5}{y}+y=25.5[/tex]
[tex]162.5+y^2 = 25.5y[/tex]
[tex]y^2 - 25.5y + 162.5 = 0[/tex]
By quadratic formula,
[tex]y=\frac{25.5\pm \sqrt{(-25.5)^2 -4\times 1\times 162.5}}{2}[/tex]
[tex]\implies y = 12.5\text{ or }y = 13[/tex]
From equation (1),
If y = 12.5,x = 13
If y = 13, x = 12.5
Hence, numbers are 12.5 and 13
