Zadanie 3
W(\sqrt5)= -x^6 -2x^5+5x^3-3x-1=-(\sqrt5)^6-2*(\sqrt5)^5+5*(\sqrt5)^3-3*\sqrt5-1=
-((\sqrt5)^2)^3-2\sqrt5*((\sqrt5)^2)^2+5\sqrt5(\sqrt5)^2-3\sqrt5-1=
-5^3-2\sqrt5*5^2+5\sqrt5*5-3\sqrt5-1=-126-28\sqrt5
Zadanie 4
a)
x^4-4x^2=x^2(x^2-4)=x^2(x-2)(x+2)
b)
4x^3-x^2+12x-3=x^2(4x-1)+3(4x-1)=(4x-1)(x^2+3)
c)
x^4-3x^3+2x^2=x^2(x^2-3x+2)=x^2(x^2-x-2x+2)=x^2[x(x-1)-2(x-1)]=x^2(x-1)(x-2)
Zadanie 5
k*(-2)^3-5(-2)^2+(2m-k)*(-2)+3m=2
k*1^3-5*1^2+(2m-k)*1+3m=-1
--------
-8k-20-4m+2k+3m=2
k-5+2m-k+3m=-1
--------
-6k-m=22
5m=4 |:5
m=\frac{4}{5}
podstawiam
-6k-\frac{4}{5}=22
-6k=22,8
k=-3,8=-\frac{19}{5}
--------
k=-\frac{19}{5}
m=\frac{4}{5}