#### Answer

3/2, 5/2

#### Work Step by Step

x+y=4
(x)(y)=15/4
x=4-y
Substitute
(4-y)(y)=15/4
4y-y^2=15/4
Rearrange
4y-y^2-15/4=0
or
y^2-4y+15/4=0
In order to get rid of denominator 4, multiply the variables and constant by 4
4(y^2-4y+15/4)=0
4y^2-16y+15=0
Using ac method a=60 b=-16
The two numbers are -10 and -6 then
4y^2-10y-6y+15=0
2y(2y-5)-3(2y-5)=0
(2y-3)(2y-5)=0
2y-3=0 2y=3 y=3/2
2y-5=0 2y=5 y=5/2
3/2+5/2=4
(3/2)(5/2)=15/4