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2(2x-3)(x+1)-5(x-1)2=2(x-2)(x-1)
2(2x2+2x-3x-3)-5(x2-2x+1)=2(x2-x-2x+2)
4x2+4x-6x-6-5x2+10x-5=2x2-2x-4x+4
4x2-5x2-2x2+4x-6x+10x+2x+4x-6-5-4=0
-3x2+14x-15=0
delta=b2-4ac= 196-180=16
pierwiastek z delty= 4
x1=-14-4/-6=3
x2=-14+4/-6=5/3=1 2/3
c)
(4-3x)2=16-9x2
16+24x+9x2=16-9x2
9x2+9x2+24x+16-16=0
18x2+24x=0
6(3x2+4x)=0
delta= 16-0=16
pierwiastek z delty=4
x1= -4-4/6=-8/6=-1 1/3
x2=-4+4/6=0
b)
(4x+1)2-(2x+1)2=(3x+1)2
16x2+8x+1-4x2-4x-1=9x2+6x+1
16x2-4x2-9x2+8x-4x-6x+1-1-1=0
3x2-2x-1=0
delta= 4+12=16
pierwiastek z delty= 4
x1=2-4/6=-1/3
x2=2+4/6=1
a)
3(x+2)2-2(x-2)(x+3)=8
3(x2+4x+4)-2(x2+3x-2x-6)=8
3x2+12x+12-2x2-6x+4x+12-8=0
3x2-2x2+12x-6x+4x+12+12-8=0
x2+10x+16=0
delta= 100-64=36
pierwiastek z delty=6
x1=-10-6/2=-8
x2=-10+6/2=-2
ale tylko jedno z nich jest niezupelne