Question

[Cứt :))]

( x - 5 )⁴ = ( x - 5 ) ⁶

^{Ai nhanh mk tk nhé}

Answer 1

[Trần Thanh Phương]

\(\left(x-5\right)^4=\left(x-5\right)^6\)

\(\left(x-5\right)^4-\left(x-5\right)^6=0\)

\(\left(x-5\right)^4-\left(x-5\right)^4\cdot\left(x-5\right)^2=0\)

\(\left(x-5\right)^4\left[1-\left(x-5\right)^2\right]=0\)

\(\Rightarrow\orbr{\begin{cases}x-5=0\\1-\left(x-5\right)^2=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=5\\x-5=\left\{\pm1\right\}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=5\\x=\left\{6;4\right\}\end{cases}}\)

Vậy \(x=\left\{4;5;6\right\}\)

Answer 2

[Kirigaya Kazuto]

\(\left(x-5\right)^4=\left(x-5\right)^6\)

\(\left(x-5\right)^6-\left(x-5\right)^4=0\)

\(\left(x-5\right)^4\left[\left(x-5\right)^2-1\right]=0\)

\(\Leftrightarrow\orbr{\begin{cases}\left(x-5\right)^4=0\\\left(x-5\right)^2-1=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x-5=0\\\left(x-6\right)\left(x-4\right)=0\end{cases}}\)

1: \(x-5=0\Leftrightarrow x=5\)

2.\(\left(x-6\right)\left(x-4\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-6=0\\x-4=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=6\\x=4\end{cases}}\)

Vậy ...