Autorzy:Wojciech Babiański, Lech Chańko, Dorota Ponczek
Wydawnictwo:Nowa Era
Rok wydania:2014
Rozwiąż równanie 4.11 gwiazdek na podstawie 9 opinii

`a)` 

`(x-5)(x+5)=x^2-100x` 

`x^2-25=x^2-100x\ \ \ |-x^2` 

`-25=-100x\ \ \ |:(-100)` 

`x=25/100=1/4` 

 

 

 

`b)` 

`(3-x)^2-(x+1/3)^2=2/9` 

`9-6x+x^2-(x^2+2/3x+1/9)=2/9` 

`9-6x+x^2-x^2-2/3x-1/9=2/9` 

`-6x-2/3x+9-1/9=2/9\ \ \ |*9` 

`-54x-6x+81-1=2` 

`-60x+80=2\ \ \ |-80` 

`-60x=-78\ \ \ |:(-60)` 

`x=78/60=39/30=13/10=1 3/10` 

 

 

`c)` 

`4(1/2x-3)^2=(2-x)^2` 

`4(1/4x^2-3x+9)=4-4x+x^2` 

`x^2-12x+36=4-4x+x^2\ \ \ |-x^2` 

`-12x+36=4-4x\ \ \ |+4x` 

`-8x+36=4\ \ \ |-36` 

`-8x=-32\ \ \ |:(-8)` 

`x=4` 

 

 

 

`d)` 

`4(x+2)^2-(2x-1)^2=-5` 

`4(x^2+4x+4)-(4x^2-4x+1)=-5` 

`4x^2+16x+16-4x^2+4x-1=-5` 

`20x+15=-5\ \ \ |-15` 

`20x=-20\ \ \ |:20` 

`x=-1` 

 

 

 

`e)` 

`(6+1/3x)(-1/3x+6)+(1/3x-4)^2=4` 

`(6+1/3x)(6-1/3x)+(1/9x^2-8/3x+16)=4` 

`36-1/9x^2+1/9x^2-8/3x+16=4` 

`36-8/3x+16=4\ \ \ \ |*3` 

`108-8x+48=12` 

`156-8x=12\ \ \ |-156` 

`-8x=-144\ \ \ |:(-8)` 

`x=18` 

 

 

`f)` 

`(-4x-3)(4x-3)+8(1-sqrt2x)^2=1`  

`-(4x+3)(4x-3)+8(1-2sqrt2x+2x^2)=1` 

`-(16x^2-9)+8-16sqrt2x+16x^2=1` 

`-16x^2+9+8-16sqrt2x+16x^2=1` 

`-16sqrt2x+17=1\ \ \ |-17` 

`-16sqrt2x=-16\ \ \ |:(-16sqrt2)` 

`x=16/(16sqrt2)=1/sqrt2=sqrt2/(sqrt2*sqrt2)=sqrt2/2`   

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