Question

(x-2)²=(x-2)⁴

Answer 1

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

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

=>\(\left(x-2\right)^2\cdot\left[\left(x-2\right)^2-1\right]=0\)

=>\(\left(x-2\right)^2\cdot\left(x-2-1\right)\left(x-2+1\right)=0\)

=>\(\left(x-2\right)^2\cdot\left(x-3\right)\left(x-1\right)=0\)

=>\(\left[{}\begin{matrix}x-2=0\\x-3=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=3\\x=1\end{matrix}\right.\)

Answer 2

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