Question

[Nguyễn Thị Bình Yên]

giải phương trình

1/ x³ + (x + 1)³ + (x + 2)³ = (x + 3)³

2/ (x + 1)⁴ + (x + 3)⁴ = 82

Answer 1

[Huy Thắng Nguyễn]

1/ \(x^3+\left(x+1\right)^3+\left(x+2\right)^3=\left(x+3\right)^3\)

\(\Leftrightarrow x^3+x^3+3x^2+3x+1+x^3+6x^2+12x+8=x^3+9x^2+27x+27\)

\(\Leftrightarrow3x^3+9x^2+15x+9=x^3+9x^2+27x+27\)

\(\Leftrightarrow2x^3-12x-18=0\)

\(\Leftrightarrow2\left(x^3-6x-9\right)=0\)

\(\Leftrightarrow2\left(x^3-3x^2+3x^2-9x+3x-9\right)=0\)

\(\Leftrightarrow2\left[x^2\left(x-3\right)+3x\left(x-3\right)+3\left(x-3\right)\right]=0\)

\(\Leftrightarrow2\left(x-3\right)\left(x^2+3x+3\right)=0\)

mà \(x^2+3x+3=\left(x+\dfrac{3}{2}\right)^2+\dfrac{3}{4}>0\forall x\)

\(\Rightarrow x-3=0\Leftrightarrow x=3\)

Vậy x = 3.