x*y=(2x-y+1)(2y-x+1)
a. Comutativitatea
x*y=y*x
(2x-y+1)(2y-x+1)=(2y-x+1)(2x-y+1)
4xy-2x²+2x-2y²+xy-y+2y-x+1=4xy-2y²+2y-2x²+xy-x+2x-y+1
5xy-2x²-2y²+x+y+1=5xy-2x²-2y²+x+y+1 Adevarat⇒legea este comutativa
b. 2m*n=13
(4m-n+1)(2n-m+1)=13
Caz 1 1×13=13
4m-n+1=1
2n-2m+1=13
4m-n=0⇒ 4m=n
8m-2m=12
6m=12⇒ m=2
n=8
Caz 2
13×1=13
4m-n+1=13
2n-2m+1=1⇒ 2n=2m⇒ n=m
4m-m=12
3m=12
m=4
n=4