Question

Tìm x biết (2x+2016)³=(x+2000)³+(x+16)³

Answer 1

Ta có : \(\left(2x+2016\right)^3=\left(x+2000\right)^3+\left(x+16\right)^3\)

=> \(\left(2x+2016\right)^3-\left(x+2000\right)^3-\left(x+16\right)^3=0\)(*)

Gọi \(a=x+2000 ; b=x+16\)

=> ;\(a+b=2x+2016\)

Từ (*) suy ra : \(\left(a+b\right)^3-a^3-b^3=0\)

=> \(3ab\left(a+b\right)=0\)

+) \(a=0\) => \(x+2000=0\) => \(x=-2000\)

+) \(b=0\) => \(x+16=0\) => \(x=-16\)

+) \(a+b=0\)=> \(2x+2016=0\) => \(x=-1008\)

  Vậy \(x\in\left\{-2000;-1008;-16\right\}\)