Matematyka

Autorzy:Maciej Antek, Krzysztof Belka, Piotr Grabowski

Wydawnictwo:Nowa Era

Rok wydania:2015

Wykonaj działania i doprowadź wynik 4.67 gwiazdek na podstawie 9 opinii
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  3. Matematyka

`a)\ 3/(sqrt7-1)-1/(sqrt3+3)-2/(sqrt7-sqrt3)=3/(sqrt7-1)*(sqrt7+1)/(sqrt7+1)-1/(sqrt3+3)*(sqrt3-3)/(sqrt3-3)-2/(sqrt7-sqrt3)*(sqrt7+sqrt3)/(sqrt7+sqrt3)=` 

`\ \ \ =(3(sqrt7+1))/(sqrt7^2-1^2)-(sqrt3-3)/(sqrt3^2-3^2)-(2(sqrt7+sqrt3))/(sqrt7^2-sqrt3^2)=(3sqrt7+3)/(7-1)-(sqrt3-3)/(3-9)-(2sqrt7+2sqrt3)/(7-3)=`  

`\ \ \ =(3sqrt7+3)/(6)-(sqrt3-3)/(-6)-(2sqrt7+2sqrt3)/4=(3sqrt7+3)/6+(sqrt3-3)/6-(sqrt7+sqrt3)/2=`   

`\ \ \ =(3sqrt7+3)/6+(sqrt3-3)/6-(3sqrt7+3sqrt3)/6=(3sqrt7+3+sqrt3-3-3sqrt7-3sqrt3)/6=(-2sqrt3)/6=-sqrt3/3` 

 

 

`b)\ 1/(sqrt7-sqrt6)-3/(sqrt6-sqrt3)-4/(sqrt7+sqrt3)=1/(sqrt7-sqrt6)*(sqrt7+sqrt6)/(sqrt7+sqrt6)-3/(sqrt6-sqrt3)*(sqrt6+sqrt3)/(sqrt6+sqrt3)-4/(sqrt7+sqrt3)*(sqrt7-sqrt3)/(sqrt7-sqrt3)=` 

`\ \ \ =(sqrt7+sqrt6)/(sqrt7^2-sqrt6^2)-(3(sqrt6+sqrt3))/(sqrt6^2-sqrt3^2)-(4(sqrt7-sqrt3))/(sqrt7^2-sqrt3^2)=(sqrt7+sqrt6)/(7-6)-(3sqrt6+3sqrt3)/(6-3)-(4sqrt7-4sqrt3)/(7-3)=` 

`\ \ \ =(sqrt7+sqrt6)/1-(3sqrt6+3sqrt3)/3-(4sqrt7-3sqrt3)/4=(sqrt7+sqrt6)-(sqrt6+sqrt3)-(sqrt7-sqrt3)=` 

`\ \ \ =sqrt7+sqrt6-sqrt6-sqrt3-sqrt7+sqrt3=0` 

 

 

`c)\ (sqrt5/(sqrt5+2)-4/(sqrt_3))^-1:(2+sqrt5)/3=(sqrt5/(sqrt5+2)*(sqrt5-2)/(sqrt5-2)-4/(sqrt5+3)*(sqrt5-3)/(sqrt5-3))^-1*3/(2+sqrt5)=` 

`\ \ \ =((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`