Autorzy:M. Braun, J. Lech
Wydawnictwo:GWO
Rok wydania:2008
Usuń niewymierność z mianownika a) 4/√ 5+24.63 gwiazdek na podstawie 8 opinii

Usuń niewymierność z mianownika a) 4/√ 5+2

34Zadanie
35Zadanie
36Zadanie
37Zadanie
1Zadanie
2Zadanie
3Zadanie
UWAGA! Oglądasz starą wersję książki. *Kilknij tutaj aby zobaczyć nową.*

a) `4/(sqrt5+2)=4/(sqrt5+2)*(sqrt5-2)/(sqrt5-2)=(4(sqrt5-2))/(sqrt5^2-2^2)=`

`=(4(sqrt5-2))/(5-4)=4sqrt5-8`

b) `2/(3-sqrt7)=2/(3-sqrt7)*(3+sqrt7)/(3+sqrt7)=(2(3+sqrt7))/(3^2-sqrt7^2)=`

`=(2(3+sqrt7))/(9-7)=(2(3+sqrt7))/2=3+sqrt7`

c) `3/(5+2sqrt5)=3/(5+2sqrt5)*(5-2sqrt5)/(5-2sqrt5)=`

`=(3(5-2sqrt5))/(5^2-(2sqrt5)^2)=(3(5-2sqrt5))/(25-20)=`

`=3/5(5-2sqrt5)=3-6/5sqrt5`

d) `10/(3sqrt2-4)=10/(3sqrt2-4)*(3sqrt2+4)/(3sqrt2+4)=`

`=(10(3sqrt2+4))/((3sqrt2)^2-4^2)=(10(3sqrt2+4))/(18-16)=`

`=(10(3sqrt2+4))/2=5(3sqrt2+4)=15sqrt2+20`

e) `sqrt3/(5sqrt3+8)=sqrt3/(5sqrt3+8)*(5sqrt3-8)/(5sqrt3-8)=`

`=(sqrt3(5sqrt3-8))/((5sqrt3)^2-8^2)=`

`=(15-8sqrt3)/(75-64)=(15-8sqrt3)/11`

f) `(2sqrt6)/(8-3sqrt6)=(2sqrt6)/(8-3sqrt6)*(8+3sqrt6)/(8+3sqrt6)=`

`=(2sqrt6(8+3sqrt6))/(8^2-(3sqrt6)^2)=`

`=(16sqrt6+36)/(64-54)=(16sqrt6+36)/10=(8sqrt6+18)/5`

g) `(1+sqrt3)/(2+sqrt3)=(1+sqrt3)/(2+sqrt3)*(2-sqrt3)/(2-sqrt3)=`

`=((1+sqrt3)(2-sqrt3))/(2^2-sqrt3^2)=`

`=(2-sqrt3+2sqrt3-3)/(4-3)=(sqrt3-1)`

h) `(sqrt5-2)/(3-sqrt5)=(sqrt5-2)/(3-sqrt5)*(3+sqrt5)/(3+sqrt5)=`

`=((sqrt5-2)(3+sqrt5))/(3^2-sqrt5^2)=`

`=(3sqrt5+5-6-2sqrt5)/(9-5)=(sqrt5-1)/4`