Question

Answer 1

`a,x^3 -y^3 +x-y`

`=(x-y)(x^2 +xy+y^2)+(x-y)`

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

`b, x^3 -y=y^3-x`

`<=>x^3 -y^3 +x-y=0`

`<=>(x-y)(x^2 +xy+y^2 +1)=0`

Ta có: 

`x^2 +xy+ y^2 +1`

`=(x^2 + 2x . y/2 + (y/2)^2 )  + (3y^2)/4 +1`

`=(x+ y/2)^2 + (3y^2)/4 +1 >0`

`=> x-y=0`

`<=>x=y`

`<=>x-y=0`

Answer 2

`a, (x^3 - y^3) + x - y`

`= (x-y)(x^2+xy+y^2) + x-y`

`= (x-y)(x^2 + xy + y^2 + 1)`.

b, `x^3 - y = y^3 - x`

`=> (x^3 - y^3) + x - y = 0`

`=> (x-y)(x^2+xy+y^2) + x - y  =0`

`=> (x-y)(x^2 + xy + y^2 - 1) = 0`

`=> {(x=y), ((x^2 + xy + y^2/4) + (3y^2)/4 + 1)}  = 0`

`=> x = y`.