Question

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

Answer 1

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

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

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

\(\Leftrightarrow2x\left(x-2\right)=0\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x-2=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x=2\end{array}\right.\)

Answer 2

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

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

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

\(\Rightarrow\left[\begin{array}{nghiempt}x=0\\x=2\end{array}\right.\)

Answer 3

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

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

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

\(\left(x-2\right).\left[\left(x+2\right)\left(x-2\right)\right]=0\)

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

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

\(\Leftrightarrow\left[\begin{array}{nghiempt}x-2=0\\2x=0\end{array}\right.\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=2\\x=0\end{array}\right.\)

Vậy \(x\in\left\{0;2\right\}\)

Answer 4

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

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

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

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

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

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

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

\(\Leftrightarrow\begin{cases}x-2=0\\2x=0\end{cases}\Leftrightarrow\begin{cases}x=2\\x=0\end{cases}\)

Vậy \(x\in\left\{0;2\right\}\)