Question

tìm x biết

x^2-4+ (x-2)^2 = 0

Answer 1

\(x^2-4+\left(x-2\right)^2=0\)
\(\Rightarrow x^2-4+x^2+4x+4=0\)
\(\Rightarrow2x^2+4x=0\)
\(\Rightarrow2x\left(x+2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}2x=0\\x+2=0\end{matrix}\right.\)            \(\Rightarrow\left[{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\)
                Vậy \(x\in\left\{0;-2\right\}\)

Answer 2

\(x^2-4+\left(x-2\right)^2=0\)

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

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

\(\Rightarrow\left(x-2\right)\left(x+2+x-2\right)=0\)

\(\Rightarrow\left(x-2\right)2x=0\)

\(\Rightarrow\left\{{}\begin{matrix}x-2=0\\2x=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=2\\x=0\end{matrix}\right.\)

Vậy ...