Question

sa se studieze asociativitstea operatiei 0 pe multimea r in cazul:a)x×y=4xy+x+y;b)x+y=xy-3(x+y)+12

Answer 1

a)caz 1

daca x=0

0×y=4×0×y+0+y

0=0+0+y⇒y=0

caz 2

daca y=0

x×0=4x×0+x+0⇒x=0

b)caz 1

daca x=0

0+y=0×y-3(0+y)+12

y=3×0-3y+12

y+3y=12

4y=12

y=12/4

y=3

daca y=0

x+0=x×0-3(x+0)+12

x=x×0-3x+12

x+3x=12

4x=12

x=12/4

x=3

Answer 2

a) x•y=4xy+x+y
6xy
b)
x+y=xy-3(x+y)+12
x+y= xy-3x-3y+12
x+y= 4x•4y+12
x+y= 8xy+12
x+y