Answer:
143
Step-by-step explanation:
Denote by x and y such integers. The hypotheses given can be written as:
[tex]x+y=24, x^2-y^2=48[/tex]
Use the difference of squares factorization to solve for x-y
[tex]48=x^2-y^2=(x-y)(x+y)=24(x-y)\text{ then }x-y=2[/tex]
Remember that
[tex](x+y)^2=x^2+2xy+y^2[/tex]
[tex](x-y)^2=x^2-2xy+y^2[/tex]
Substract the second equation from the first to obtain
[tex](x+y)^2-(x-y)^2=4xy[/tex]
Substituting the known values, we get
[tex]4xy=24^2-2^2=572\text{ then }xy=\frac{572}{4}=143[/tex]
