Question

Pe multimea numerelor reale se defineste legea de compozitie x o y= xy + 4x + 4y + 12
a) Aratati ca x o y = (x + y) (y + 4) - 4, pt orice numere reale x si y
b) Rezolvati in multimea nr reale ecuatia x o x= x

Answer 1

[tex]\it x\circ y =xy+4x+4y+12 = xy+4x+4y+16-4 = \\\;\\ =(xy+4y) +(4x+16) -4=y(x+4) +4(x+4)-4 = \\\;\\ = (x+4)(y+4)-4[/tex]

[tex]\it x\circ x =x \Leftrightarrow (x+4)(x+4) -4 =x \Leftrightarrow (x+4)(x+4) -(x+ 4)=0 \\\;\\ \Leftrightarrow (x+4)(x+3) = 0 \Leftrightarrow x= -4\ \ sau\ \ x = -3 [/tex]

Answer 2

.......................................................