Question

Se da legea de copozitie: x*y=xy-2x-2y+6 a) Aratati ca: x*y=(x-2)(y-2)+2
b) Rezolvati ecuatia: x*x*x=x ​

Answer 1

Răspuns:

Explicație pas cu pas:

a.  x*y=xy-2x-2y+6

x*y=xy-2x-2y+4+2

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

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

b. x*x*x=x

x*x=(x-2)(x-2)+2=(x-2)²+2

x*x*x=[(x-2)²+2]*x=[(x-2)²+2-2](x-2)+2

x*x*x=(x-2)³+2

(x-2)³+2=x

(x-2)³-(x-2)=0

(x-2)[(x-2)²-1]=0

x₁=2

(x-2)²-1=0

x²-4x+3=0

Δ=16-12=4

x₂=3

x₃=1