Question

Pe R definim legile de compozitie x○y=x + y + 3 si x * y = xy -3 (x+y)+ 12
Rezolvati in R ecuatia x○(x+1)+x * (x+1) 11.​

Answer 1

$x\circ y=x+y+3\\x*y=xy-3(x+y)+12=xy-3x-3y+9+3=x(y-3)-3(y-3)+3=\\(x-3)(y-3)+3\\\\x\circ(x+1)+x*(x+1)=11\\x+x+1+3+(x-3)(x+1-3)+3=11\\2x+(x-3)(x-2)+7=11\\x^2-3x+2=0\Rightarrow x_1=1\overset{Vi\'ete}{\Longrightarrow}x_2=2\\\matcal{S}=\{1, 2\}$