Question

Usuń niewymierność: 1/(1-2^(1/3)+4^(1/3))

2^(1/3) - pierwiastek 3 stopnia z 2

1 jest w liczniku

, a nawias w mianowniku

Answer 1

1/(1-2^(1/3)+4^(1/3))=

[1/(1-2^(1/3)+4^(1/3))]*(1+2^(1/3))=(1+2^(1/3))/(1^3+(2^(1/3))^3)=

(1+2^(1/3))/(1+2)=(1+2^(1/3))/3=1/3+1/3*2^(1/3)