[tex]x*y=xy-k(x+y)+k^2+k[/tex]
a) [tex]2*3=2*3-k(2+3)+k^2+k=2
6-5k+k^2+k=2
k^2-4k+4=0
(k-2)^2=0
k=2[/tex]
b)[tex]x*y=xy-2(x+y)+6=6
x^2-4x+6=6
x^2-4x=0
x(x-4)=0
x=0 sau x-4=0 x=4
[/tex]
c)[tex]x[/tex]∈M Din astea doua dă [tex]x[/tex]∈ [tex][k, \infty][/tex]
[tex]y[/tex]∈M [tex]y[/tex]∈ [tex][k, \infty][/tex]
[tex]x \geq k =\ \textgreater \ \ \textgreater \ x-k \geq 0
y \geq k=\ \textgreater \ \ \textgreater \ y-k \geq 0
(x-k)*(y-k) \geq 0
xy-xk-yk+k^2 \geq 0
xy-k(x+y)+k^2 \geq 0 / +k
xy-k(x+y)+k^2 \geq k
==\ \textgreater \ \ \textgreater \ \ \textgreater \ x*y[/tex]∈[tex]M ,[/tex]∀[tex]x,y[/tex]∈M
