Odpowiedź:
ZAD 1
Równanie x(x-2)²=(x-2)²
x(x-2)²-(x-2)²=0
(x-2)²(x-1)=0
(x-2)²=0⇒x=2
x-1=0⇒x=1
odp.D
ZAD 2
x²-6x+9=(x+3)²=(6+3)²=9
x²-6*x+9=6²-6*6+9=36-36+9=9
Zad 3
x(x-3)(x+2)=0
x=0
x-3=0⇒x=3
x+2=0⇒x=-2
suma
0+3+(-2)=3-2=1
Odp. B
Zad 4
2(x-1)(x+3)>x-1
2(x-1)(x+3)-(x-1)>0
(x-1)(2(x+6)-1)>0
(x-1)(2x+5)>0
[tex]\left \{ {{x-1>0} \atop {2x+5>0}} \right.[/tex]
[tex]\left \{ {{x-1<0} \atop {2x+5<0}} \right.[/tex]
[tex]\left \{ {{x>1} \atop {x>-5/2}} \right.[/tex]
[tex]\left \{ {{x<1} \atop {x<-5/2}} \right.[/tex]
x∈<-∞,-5/2>∪<1,+∞>
albo
2(x-1)(x+3)>x-1
2x²+6x-2x-6>x-1
2x²+3x-5>0
Δ=49
√Δ=7
x₁=-5/2
x₂=1
Zad 5
(x²-1)(x²-2x)=0
x²-1=0 ⇒ x=1 i x=-1
x²-2x=0 ⇒ x=0 i x=2
Odp: x=-1,x=0,x=1,x=2
Szczegółowe wyjaśnienie: