Answer: [tex](12,-3)\ \text{or}\ (3,-12)[/tex]
Step-by-step explanation:
Given
The product of integers is -36
The difference of integers is 15
Suppose the integers are x and y
[tex]\Rightarrow x-y=15\\\Rightarrow x=15+y\\\Rightarrow xy=-36[/tex]
Put the value of [tex]x[/tex] in the product
[tex]\Rightarrow (15+y)y=-36\\\Rightarrow 15y+y^2+36=0\\\Rightarrow y^2+12y+3y+36=0\\\Rightarrow y(y+12)+3(y+12)=0\\\Rightarrow (y+12)(y+3)=0\\\Rightarrow y=-3\ \text{or}\ -12[/tex]
[tex]\therefore x=12\ \text{or}\ 3[/tex]
Pairs of integers are [tex](12,-3)\ \text{or}\ (3,-12)[/tex]
