Question

1).Pe R se defineste legea de compoziție x*y=x+y+1.Sa se rezolve ecuatia x la a doua *x*x=1
2).Pe R se definește legea de compoziție x*y=2xy-6x-6y+21.Sa se rezolve ecuatia x*(x+1)=7

Answer 1

[tex]x*y=x+y+1 x^2*x= x^2+x+1 x^2+x+1*x=x^2+x+1+x+1-1=0 x^2+2x+1=0[/tex]
Stii sa o rezolvi e ecuatie de gradul 2

[tex]x*y=2xy-6x-6y+21 x*(x+1) 2x(x+1)-6x-6(x+1)+21-7=0 2x^2+2x-6x-6x-6+21-7=0 2x^2-10x+8=0[/tex]

Tot asa delta si radacini

Answer 2

1) x * y = x + y + 1
x² * x * x = 1
Grupam astfel termenii: x² * (x * x) = 1
x² * (x + x + 1) = 1 , x² * (2x + 1) = 1 , x² + 2x + 1 + 1 = 1 ,
x² + 2x + 2 = 1 , x² + 2x + 1 = 0 , x² + x + x + 1 = 0 , x (x + 1) + (x + 1) = 0 ,
(x + 1)² = 0 , de unde x = -1.

2) x * y = 2xy - 6x - 6y + 21
x * (x + 1) = 7
2x (x + 1) - 6x - 6 (x + 1) + 21 = 7 , 2x² + 2x - 6x - 6x - 6 + 21 = 7 ,
2x² - 10x + 15 = 7 , 2x² - 10x + 8 = 0  | : 2 , x² - 5x + 4 = 0 , x² - x - 4x + 4 = 0
x (x - 1) - 4 (x - 1) = 0 , (x - 4) (x - 1) = 0 , de unde x 1 = 4 si x 2 = 1.