Question

fie legea de compozitie.. va rog punctele c si d. Multumesc!

Answer 1

a)

x*y=xy-3x-3y+12=x(y-3)-3(y-3)+3=(x-3)(y-3)+3

b)

Folosim forma legii determinata la punctul a).

x*x=(x-3)(x-3)+3=(x-3)²+3

x*x=x

(x-3)²+3=x

(x-3)²+3-x=0

(x-3)²-(x-3)=0

(x-3)(x-3)-(x-3)=0

(x-3)(x-3-1)=0

(x-3)(x-4)=0

x-3=0 => x1=3

x-4=0 => x2=4

x∈{3;4}

c)

Observam ca:

a*3=(a-3)(3-3)+3=(a-3)*0+3=3

3*b=(3-3)(b-3)+3=0*(b-3)+3=3

Notam: 1*2=a si 4*5*...*2018=b si avem:

1*2*3*....*2018=a*3*b

Si tinand cont de cele de mai sus:

1*2*3*....*2018=a*3*b=3*b=3

d)

Observam ca:

c*3=(c-3)(3-3)+3=(c-3)*0+3=3

3*d=(3-3)(d-3)+3=0*(d-3)+3=3

√36/2=6/2=3

Notam: c=√1/2*√2/2*......*√35/2 si d=√37/2*√38/2*.......*√2018/2 si avem (cu toate explicatiile de la pct c si d):

√1/2*√2/2*......*√35/2*√36/2*√37/2*√38/2*.......*√2018/2=c*3*d=3*d=3