Matematyka
 
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Autorzy: Maciej Antek, Krzysztof Belka, Piotr Grabowski
Wydawnictwo: Nowa Era
Rok wydania: 2015
Wykonaj działania i doprowadź wynik 4.5 gwiazdek na podstawie 6 opinii

 

  

   

 

 

 

 

 

 

 

 

 

 

`\ \ \ =((sqrt5(sqrt5-2))/(sqrt5^2-2^2)-(4(sqrt5-3))/(sqrt5^2-3^2))^-1*3/(2+sqrt5)*(2-sqrt5)/(2-sqrt5)=((5-2sqrt5)/(5-4)-(4(sqrt5-3))/(5-9))^-1*(3(2-sqrt5))/(2^2-sqrt5^2)=` 

`\ \ \ =((5-2sqrt5)/1-(strike4^1(sqrt5-3))/-strike4^1)^-1*(6-3sqrt5)/(4-5)=(5-2sqrt5+sqrt5-3)^-1*(6-3sqrt5)/(-1)=` 

`\ \ \ =(2-sqrt5)^-1*(3sqrt5-6)=1/(2-sqrt5)*(3sqrt5-6)=(3sqrt5-6)/(2-sqrt5)=(3sqrt5-6)/(2-sqrt5)*(2+sqrt5)/(2+sqrt5)=` 

`\ \ \ =(6sqrt5+3*5-12-6sqrt5)/(2^2-sqrt5^2)=3/(4-5)=3/(-1)=-3` 

 

 

`d)\ (2/(sqrt3-1)+3/(sqrt3-2)+15/(3-sqrt3))^-1*(sqrt3+5)=(2/(sqrt3-1)*(sqrt3+1)/(sqrt3+1)+3/(sqrt3-2)*(sqrt3+2)/(sqrt3+2)+15/(3-sqrt3)*(3+sqrt3)/(3+sqrt3))^-1*(sqrt3+5)=` 

`\ \ \ =((2sqrt3+2)/(sqrt3^2-1^2)+(3sqrt3+6)/(sqrt3^2-2^2)+(45+15sqrt3)/(3^2-sqrt3^2))^-1*(sqrt3+5)=((2sqrt3+2)/(3-1)+(3sqrt3+6)/(3-4)+(45+15sqrt3)/(9-3))^-1*(sqrt3+5)=` 

`\ \ \ =((2sqrt3+2)/2+(3sqrt3+6)/(-1)+(45+15sqrt3)/(6))^-1*(sqrt3+5)=(sqrt3+1-3sqrt3-6+7,5+2,5sqrt3)^-1*(sqrt3+5)=` 

`\ \ \ =(0,5sqrt3+2,5)^-1*(sqrt3+5)=1/(0,5sqrt3+2,5)*(sqrt3+5)=(sqrt3+5)/(0,5sqrt3+2,5)=(sqrt3+5)/(0,5(sqrt3+5))=1/(0,5)=10/5=2`