a) (-3)o5 = -15 +12-16 +20 =1
b) xy -4x-4y+20 = xy -4x-4y+16+4 =x(y-4) -4(y-4) +4 =
= (x-4)(y-4) +4
c) x o x =x
x^2 -4x-4x+20 =x => x^2 -x+20 =0
calculam delta : 1-2x20 =1-80=-79
Deoarece delta < 0 , ecuatia nu are radacini reale.
(2x+5) o (4x+3) = 4 => (2x+5)(4x+3) -4(2x+5) -4(4x+3) +20 =4
8x^2 +20x+6x+15 -8x-20 -16x-12 +20 -4 =0
8x^2 +2x -1 =0
calculam delta: 4+4x8x1=36
x1 =(-2+6)/16 =1/4
x2 =(-2 -6)/16= -1/2
d) (x o y) o z =x o (y o z)
( x o y ) o z = (xy-4x-4y+20) o z = xyz -4xz-4yz+20z-4xy+16x+16y-80-4z+20
= xyz-4xy-4xz-4yz+4(x+y+z) -60
x o (y o z)= x o (yz-4y-4z+20) =xyz-4xy-4xz+20x-4x-4yz+16y+16z-80+20
=xyz-4xy-4xz-4yz+4(x+y+z)-60
Deci (x o y) o z =x o (y o z) si legea este asociativa
Elementul neutru:
x o e = e o x = x
x o e = xe-4x-4e+20 =x
e(x-4) =5x -20
e(x-4) = 5(x-4)
e = 5(x-4)/(x-4)
e =5
