1
(2x²+3x-1)-5(2x²+3x-1)+4=0
2x²+3x-1=a
a²-4a+4=0
a1+a2=5 U a1*a2=4
a1=1⇒2x²+3x-1=1
2x²+3x-2=0
D=9+16=25
x1=(-3-5)/4=-2 U x2=(-3+5)/4=0,5
a2=4⇒2x²+3x-1=4
2x²+3x-5=0
D=9+40=49
x3=(-3-7)/4=-2,5 U x4=(-3+7)/4=1
x={-2,5;-2;0,5;1}
2
(x²+9x)(x²+9x+20)+96=0
x²+9x=a
a(a+20)+96=0
a²+20a+96=0
a1+a2=-20 U a1*a2=96
a1=-12⇒x²+9x=-12
x²+9x+12=0
D=81-36=45
x1=(-9-3√5)/2 U x2=(-9+3√5)/2
a2=-8⇒x²+9x=-8
x²+9x+8=0
x3+x4=-9 U x3*x4=8
x3=-8 U x4=-1
x={-4,5-1,5√5;-4,5+1,5√5;-8;-1}
3
3/(x²-4x+1)-(x²-4x+1)-2=0
x²-4x+1=a
3/a-a-2=0
a²+2a-3=0
a1+a2=-2 U a1*a2=-3
a1=-3⇒x²-4x+1=-3
x²-4x+4=0
(x-2)²=0
x=2
a2=1⇒x²-4x+1=1
x²-4x=0
x(x-4)=0
x=0
x=4
x={0;2;4}
4
6(x²+1/x²)+5(x+1/x)-38=0
6(x+1/x)²-12+5(x+1/x)-38=0
(x+1/x)=a
6a²+5a-50=0
D=25+1200=1225
a1=(-5-35)/12=-10/3⇒x+1/x=-10/3
3x²+10x+3=0,x≠0
D=100-36=64
x1=(-10-8)/6=-3
x2=(-10+8)/6=-1/3
a2=(-5+35)/12=5/2⇒x+1/x=5/2
2x²-5x+2=0,x≠0
D=25-16=9
x3=(5-3)/4=1/2
x4=(5+3)/4=2
x={-1/3;-3;1/2;2}