Ответ:

[tex](9;-10),\ (3;-3),\ (3;2),\ (9;9),\ (-11;-10),\ (-5;-3),\ (-5;2),\ (-11;9)[/tex]

Пошаговое объяснение:

[tex]n^2-m^2=2m-n-9[/tex]

[tex]n^2+n-m^2-2m+9=0[/tex]

[tex]n^2+n+\frac{1}{4}-m^2-2m-1+9\frac{3}{4}=0[/tex]

[tex]\left( n+\frac{1}{2}\right)^2-(m+1)^2+9\frac{3}{4}=0[/tex]

[tex]\left( n+\frac{1}{2}\right)^2-(m+1)^2=-\frac{39}{4}\ \ \ |\cdot 4[/tex]

[tex]\left(2n+1\right)^2-(2m+2)^2=-39[/tex]

[tex](2n+1-2m-2)(2n+1+2m+2)=-39[/tex]

[tex](2n-2m-1)(2n+2m+3)=-39[/tex]

1.

[tex](2n-2m-1)(2n+2m+3)=-39\cdot 1[/tex]

[tex]\begin{cases}2n-2m-1=-39\\2n+2m+3=1 \end{cases}[/tex]

[tex]\begin{cases}2n-2m=-39+1\\2n+2m=1-3 \end{cases}[/tex]

[tex]\begin{cases}2n-2m=-38\\2n+2m=-2 \end{cases}[/tex]

+_________________

[tex]4n=-40\ \ \ |:4[/tex]

[tex]n=-10[/tex]

[tex]2n+2m=-2[/tex]

[tex]2\cdot(-10)+2m=-2[/tex]

[tex]-20+2m=-2[/tex]

[tex]2m=-2+20[/tex]

[tex]2m=18\ \ \ |:2[/tex]

[tex]m=9[/tex]

[tex](9;-10)[/tex]

==============================

2.

[tex](2n-2m-1)(2n+2m+3)=-13\cdot 3[/tex]

[tex]\begin{cases}2n-2m-1=-13\\2n+2m+3=3 \end{cases}[/tex]

[tex]\begin{cases}2n-2m=-13+1\\2n+2m=3-3 \end{cases}[/tex]

[tex]\begin{cases}2n-2m=-12\\2n+2m=0 \end{cases}[/tex]

+_________________

[tex]4n=-12\ \ \ |:4[/tex]

[tex]n=-3[/tex]

[tex]2n+2m=0[/tex]

[tex]2\cdot(-3)+2m=0[/tex]

[tex]-6+2m=0[/tex]

[tex]2m=0+6[/tex]

[tex]2m=6\ \ \ |:2[/tex]

[tex]m=3[/tex]

[tex](3;-3)[/tex]

==============================

3.

[tex](2n-2m-1)(2n+2m+3)=-3\cdot 13[/tex]

[tex]\begin{cases}2n-2m-1=-3\\2n+2m+3=13 \end{cases}[/tex]

[tex]\begin{cases}2n-2m=-3+1\\2n+2m=13-3 \end{cases}[/tex]

[tex]\begin{cases}2n-2m=-2\\2n+2m=10 \end{cases}[/tex]

+_________________

[tex]4n=8\ \ \ |:4[/tex]

[tex]n=2[/tex]

[tex]2n+2m=10[/tex]

[tex]2\cdot2+2m=10[/tex]

[tex]4+2m=10[/tex]

[tex]2m=10-4[/tex]

[tex]2m=6\ \ \ |:2[/tex]

[tex]m=3[/tex]

[tex](3;2)[/tex]

==============================

4.

[tex](2n-2m-1)(2n+2m+3)=-1\cdot 39[/tex]

[tex]\begin{cases}2n-2m-1=-1\\2n+2m+3=39 \end{cases}[/tex]

[tex]\begin{cases}2n-2m=-1+1\\2n+2m=39-3 \end{cases}[/tex]

[tex]\begin{cases}2n-2m=0\\2n+2m=36 \end{cases}[/tex]

+_________________

[tex]4n=36\ \ \ |:4[/tex]

[tex]n=9[/tex]

[tex]2n+2m=36[/tex]

[tex]2\cdot9+2m=36[/tex]

[tex]18+2m=36[/tex]

[tex]2m=36-18[/tex]

[tex]2m=18\ \ \ |:2[/tex]

[tex]m=9[/tex]

[tex](9;9)[/tex]

==============================

5.

[tex](2n-2m-1)(2n+2m+3)=1\cdot (-39)[/tex]

[tex]\begin{cases}2n-2m-1=1\\2n+2m+3=-39 \end{cases}[/tex]

[tex]\begin{cases}2n-2m=1+1\\2n+2m=-39-3 \end{cases}[/tex]

[tex]\begin{cases}2n-2m=2\\2n+2m=-42 \end{cases}[/tex]

+_________________

[tex]4n=-40\ \ \ |:4[/tex]

[tex]n=-10[/tex]

[tex]2n+2m=-42[/tex]

[tex]2\cdot(-10)+2m=-42[/tex]

[tex]-20+2m=-42[/tex]

[tex]2m=-42+20[/tex]

[tex]2m=-22\ \ \ |:2[/tex]

[tex]m=-11[/tex]

[tex](-11;-10)[/tex]

==============================

6.

[tex](2n-2m-1)(2n+2m+3)=3\cdot (-13)[/tex]

[tex]\begin{cases}2n-2m-1=3\\2n+2m+3=-13 \end{cases}[/tex]

[tex]\begin{cases}2n-2m=3+1\\2n+2m=-13-3 \end{cases}[/tex]

[tex]\begin{cases}2n-2m=4\\2n+2m=-16 \end{cases}[/tex]

+_________________

[tex]4n=-12\ \ \ |:4[/tex]

[tex]n=-3[/tex]

[tex]2n+2m=-16[/tex]

[tex]2\cdot(-3)+2m=-16[/tex]

[tex]-6+2m=-16[/tex]

[tex]2m=-16+6[/tex]

[tex]2m=-10\ \ \ |:2[/tex]

[tex]m=-5[/tex]

[tex](-5;-3)[/tex]

==============================

7.

[tex](2n-2m-1)(2n+2m+3)=13\cdot (-3)[/tex]

[tex]\begin{cases}2n-2m-1=13\\2n+2m+3=-3 \end{cases}[/tex]

[tex]\begin{cases}2n-2m=13+1\\2n+2m=-3-3 \end{cases}[/tex]

[tex]\begin{cases}2n-2m=14\\2n+2m=-6 \end{cases}[/tex]

+_________________

[tex]4n=8\ \ \ |:4[/tex]

[tex]n=2[/tex]

[tex]2n+2m=-6[/tex]

[tex]2\cdot2+2m=-6[/tex]

[tex]4+2m=-6[/tex]

[tex]2m=-6-4[/tex]

[tex]2m=-10\ \ \ |:2[/tex]

[tex]m=-5[/tex]

[tex](-5;2)[/tex]

==============================

8.

[tex](2n-2m-1)(2n+2m+3)=39\cdot (-1)[/tex]

[tex]\begin{cases}2n-2m-1=39\\2n+2m+3=-1 \end{cases}[/tex]

[tex]\begin{cases}2n-2m=39+1\\2n+2m=-1-3 \end{cases}[/tex]

[tex]\begin{cases}2n-2m=40\\2n+2m=-4 \end{cases}[/tex]

+_________________

[tex]4n=36\ \ \ |:4[/tex]

[tex]n=9[/tex]

[tex]2n+2m=-4[/tex]

[tex]2\cdot9+2m=-4[/tex]

[tex]18+2m=-4[/tex][tex]2m=-4-18[/tex]

[tex]2m=-22\ \ \ |:2[/tex]

[tex]m=-11[/tex]

[tex](-11;9)[/tex]