`(x^3+1):(x^2-x+1)`

`=[(x+1)(x^2-x+1)]:(x^2-x+1)`

`=x+1`

`sqrt{x-3}+root{3}{x+4}=3(x>=3)`

`<=>sqrt{x-3}-1+root{3}{x+4}-2=0`

`<=>(x-3-1)/(sqrt{x-3}+1)+(x+4-8)/(root{3}{(x+4)^2}+2root{3}{x+4}+4)=0`

`<=>(x-4)/(sqrt{x-3}+1)+(x-4)/(root{3}{(x+4)^2}+2root{3}{x+4}+4)=0`

`<=>(x-4)(1/(sqrt{x-3}+1)+1/(root{3}{(x+4)^2}+2root{3}{x+4}+4))=0`

Mà `1/(sqrt{x-3}+1)+1/(root{3}{(x+4)^2}+2root{3}{x+4}+4)>0AAx>=3`

`<=>x-4=0<=>x=4(tmdk)`

`->S={4}`

Tách thành các hạng tử

`2x^3-3x^2+2x-1`

`=2x^3-2x^2-x^2+x+x-1`

`=2x^2(x-1)-x(x-1)+x-1`

`=(x-1)(2x^2-x+1)`

`B=x(2x-1)`

`=2x(x-1/2)`

`=2(x^2-1/2x)`

`=2(x^2-1/2x+1/16)-1/8`

`=2(x-1/4)^2-1/8>=-1/8`

Dấu "=" xảy ra khi `x=1/4`

`C=x(3x+4)`

`=3x(x+4/3)`

`=3(x^2+4/3x)`

`=3(x^2+4/3x+4/9)-4/3`

`=3(x+2/3)^2-4/3>=-4/3`

Dấu "=" xảy ra khi `x=-2/3`

Giải PT lượng giác:

`sin(x/2-sinx)=sin^2(x/2)`