1)x²(x²-4x+4)-(x²-2x+1)=0
x²(x-2)²-(x-1)²=0
[x(x-2)-(x-1)]*[x(x-2)+9x-1)]=0
(x²-2x-x+1)(x²-2x+x-1)=0
(x²-3x+1)=0
D=9-4=5
x1=(3-√5)/2 U x2=(3+√5)/2
x²-x-1=0
D=1+4=5
x3=(1-√5)/2 U x2=(1+√5)/2
2)[(x-1)(x-4)]*[(x-2)(x-3)]-8=0
(x²-5x+4)(x²-5x+6)-8=0
x²-5x+4=a
a(a+2)-8=0
a²+2a-8=0
a1+a2=-2 U a1*a2=-8
a1=-4⇒x²-5x+4=-4⇒x²-5x+8=0⇒D=25-32=-7<0 нет решения<br>a2=2⇒x²-5x+4=2⇒x²-5x+2=0
D=25-8=17
x1=(5-√17)/2 U x2=(5+√17)/2
3)(x²+x+1)²-2(x²+x+1)-24=0
x²+x+1=a
a²-2a-24=0
a1+a2=2 U a1*a2=-24
a1=-4⇒x²+x+1=-4⇒x²+x+5=0⇒D=1-20=-19<0 нетрешения<br>a2=6⇒x²+x+1=6⇒x²+x-5=0
D=1+20=21
x1=(-1-√21)/2 U x2=(-1+√21)/2
4)x²(x+2)-(x+2)=0
(x+2)(x²-1)=0
(x+2)(x-1)(x+1)=0
x+2=0⇒x=-2
x-1=0⇒x=1
x+1=0⇒x=-1