Giải phương trình bậc 3

S

sayhi

$(x−1)^3+x^3+(x+1)^3=(x+2)^3$
$<=>(x-1)^3 +(x+1)^3 =(x+2)^3 -x^3$
$<=>2x.[(x-1)^2 +(x+1)^2 -(x-1)(x+1)]=2.[x^2 +x(x+2)+ (x+2)^2]$
$<=>x.(x^2 +3) =3x^2 +6x +4$
$<=>x^3-3x^2 -3x -4=0$
$<=>x^3 -4x^2 +x^2 -4x +x-4=0$
$<=>(x-4)(x^2 +x+1)=0$
$<=>x=4 $
 
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