Autorzy:Wojciech Babiański, Lech Chańko, Dorota Ponczek
Wydawnictwo:Nowa Era
Rok wydania:2014
Oblicz 4.72 gwiazdek na podstawie 7 opinii

`a)\ (2+sqrt2)^3=2^3+3*2^2*sqrt2+3*2*sqrt2^2+sqrt2^3=` 

`\ \ \ =8+3*4*sqrt2+3*2*2+2sqrt2=` 

`\ \ \ =8+12sqrt2+12+2sqrt2=` 

`\ \ \ =20+14sqrt2` 

 

 

 

`b)\ (sqrt5-1)^3=sqrt5^3-3*sqrt5^2*1+3*sqrt5*1^2-1^3=` 

`\ \ \ =5sqrt5-3*5*1+3sqrt5-1=`  

`\ \ \ =5sqrt5-15+3sqrt5-1=`  

`\ \ \ =8sqrt5-16` 

 

 

 

`c)\ (3-sqrt3)^3=3^3-3*3^2*sqrt3+3*3*sqrt3^2-sqrt3^3=` 

`\ \ \ =27-3*9sqrt3+3*3*3-3sqrt3=` 

`\ \ \ =27-27sqrt3+27-3sqrt3=` 

`\ \ \ =54-30sqrt3` 

 

 

 

`d)\ (sqrt2-4)^3=sqrt2^3-3*sqrt2^2*4+3*sqrt2*4^2-4^3=` 

`\ \ \ =2sqrt2-3*2*4+3*sqrt2*16-64=` 

`\ \ \ =2sqrt2-24+48sqrt2-64=` 

`\ \ \ =50sqrt2-88` 

 

 

 

`e)\ (1+2sqrt5)^3=1^3+3*1^2*2sqrt5+3*1*(2sqrt5)^2+(2sqrt5)^3=`  

`\ \ \ =1+3*1*2sqrt5+3*1*4*5+8*5sqrt5=` 

`\ \ \ =1+6sqrt5+60+40sqrt5=` 

`\ \ \ =46sqrt5+61` 

 

 

 

`f)\ (2sqrt3-3)^3=(2sqrt3)^3-3*(2sqrt3)^2*3+3*2sqrt3*3^2-3^3=` 

`\ \ \ =8*3sqrt3-3*4*3*3+3*2sqrt3*9-27=` 

`\ \ \ =24sqrt3-108+54sqrt3-27=` 

`\ \ \ =78sqrt3-135` 

 

 

 

`g)\ (sqrt2+sqrt3)^3=sqrt2^3+3*sqrt2^2*sqrt3+3*sqrt2*sqrt3^2+sqrt3^3=` 

`\ \ \ =2sqrt2+3*2*sqrt3+3*sqrt2*3+3sqrt3=` 

`\ \ \ =2sqrt2+6sqrt3+9sqrt2+3sqrt3=` 

`\ \ \ =11sqrt2+9sqrt3` 

 

 

 

`h)\ (sqrt3-sqrt6)^3=sqrt3^3-3*sqrt3^2*sqrt6+3*sqrt3*sqrt6^2-sqrt6^3=` 

`\ \ \ =3sqrt3-3*3*sqrt6+3*sqrt3*6-6sqrt6=` 

`\ \ \ =3sqrt3-9sqrt6+18sqrt3-6sqrt6=`  

`\ \ \ =21sqrt3-15sqrt6`