Question

Exercitiul 9 va rog urgent a, b

Answer 1

vezi rezolvarea in poza!

Answer 2

$a) x \circ x\circ x\circ x=-2 \\\\ (x+x+2)\circ x\circ x=-2\\\\ (2x+2)\circ x\circ x=-2 \\\\ (2x+2+x+2)\circ x=-2 \\\\ (3x+4) \circ x=-2 \\\\ 3x+4+x+2=-2 \\\\ 4x+6=-2 \\\\ 4x=-8 \\\\ \boxed{x = -2}$

$b) \circ - \hbox{asociativa} \iff x\circ(y\circ z)= (x\circ y) \circ z \ \ ; \ \ \forall \ x,y,z \in R \\\\\\ x\circ ( y \circ z)= x \circ ( y+z+2)= x+y+z+2+2= x+y+z+4 \ \ (1) \\\\\\ (x \circ y) \circ z= (x+y+2) \circ z= x+y+2+z+2 = x+y+z+4 \ \ (2) \\\\\\ \hbox { Din (1) \land \ (2) \implies \circ - \hbox{asociativa}$