Question

pe multimea numerelor reale se defineste legea compozitie xoy=xy+2x+2y+2.a) Aratati ca 1 compus(-2)=-2. b)demonstrati ca xoy=(x+2)(y+2)-2,pentru orice numere reale x si y.c)determinati numerele reale nenule x,pentru care xo 1 pe x= x

Answer 1

xoy=xy+2x+2y+2

a) 1o(-2)=-2+2+-4+2=-2

b) xoy

=xy+2x+2y+2

= (xy+2x)+(2y+4)-2

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

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

c) xo(1/x)= x ; x≠0

xo(1/x)

=x•(1/x)+2x+2•(1/x)+2

=1+2x+2/x+2

=2x+3+ 2/x

=(2x²+3x+2)/x

egalam cele doua relatii:

(2x²+3x+2)/x=x

=> 2x²+3x+2=x²

x²+3x+2=0

Δ =9-8=1

x1=(-3-1)/2=-2

x2=(-3+1)/2=-1

x∈{-2; -1}