Question

Ajutorrr nu ma descurc deloc

Answer 1

xoy=2xy-6x-6y+21, (∀) x,y ∈ R.

a) 3o1/2=2·(3)·(1/2)-6·(3)-6·(1/2)+21=6-18-3+21=3.

b) xoy=2xy-6x-6y+21=2xy-6x-6y+18+3=2(xy-3x-3y+9)+3=

2(x(y-3)-3(y-3))+3=2(x-3)(y-3)+3.

c) legea ''o'' este asociativa daca (xoy)oz=xo(yoz).

(xoy)=α, (xoy)oz=αoz=2(α-3)(z-3)+3=2[2(x-3)(y-3)+3)-3](z-3)+3=

(4xy-12x-12y+36)(z-3)+3=4xyz-12xy-12xz+36x-12yz+36y+36z-105.

(yoz)=β, xo(yoz)-xoβ=2(x-3)(β-3)+3=(2x-6)(2yz-6y-6z+18)+3=

4xyz-12xy-12xz+36x-12yz+36y+36z-105.

asadar, (xoy)oz=xo(yoz)=4xyz-12xy-12xz+36x-12yz+36y+36z-105.

prin urmare, legea ''o'' este asociativa.