Question

Pe multimea numerelor reale se defineste legea de compozitie x o y = x + y + xy.
a) Aratati ca x o y = ( x + 1 ) ( y + 1 ) - 1 pentru orice numere reale x si y
b) Rezolvati in multimea numerelor reale ecuatia ( x + 1 ) o ( x - 3) = 4

Answer 1

Sper sa se inteleaga.

Answer 2

a)

[tex]\it x\circ y =x+y+xy = x+y+xy +1-1= (x + 1) + (y + xy) - 1 = \\\;\\ =(x+1) +y(x+1) -1 =(x+1)(1+y)-1 =(x+1)(y+1) - 1[/tex]

b)

[tex]\it (x+1)\circ(x-3) =4 \Leftrightarrow (x+1+1)(x-3+1) -1 = 4\Leftrightarrow \\\;\\ \Leftrightarrow (x+2)(x-2) -1 =4 \Leftrightarrow x^2-4-1=4 \Leftrightarrow x^2=9 \Leftrightarrow \\\;\\ \Leftrightarrow x=\pm3[/tex]