Question

tìm x biết 

\(x+2\sqrt{2x^2}+2x^3=0\)

Answer 1

\(x+2\sqrt{2x^2}+2x^3=0\\ x+2.\sqrt{2}.x+2x^3=0\\ x+1.x+2x^3=0\\ 2x+2x^3=0\\ 2x\left(1+x^2\right)=0\)

ta thấy \(x^2+1>0\)nên để \(2x\left(1+x^2\right)=0\)thì 2x=0 vậy x=0

Answer 2

\(x+2\sqrt{2x^2}+2x^3=0\)

\(\Rightarrow\)\(x\left(1+\sqrt{2x}+2x^2\right)=0\)

\(x=0\)( 1 ) hoặc \(\left(1+\sqrt{2x}+2x^2\right)=0\)( 2 )

\(2\Leftrightarrow\left(1+\sqrt{2x}\right)^2=0\)

\(\Rightarrow\)\(x=\frac{-1}{\sqrt{2}}\Rightarrow x=\frac{-\sqrt{2}}{2}\)

Vậy \(x=0;x=\frac{-\sqrt{2}}{2}\)