a)Ta có:04=06
14=16
(-1)4=(-1)6
=>x-5 E {-1;0;1}
=>x E {4;5;6}
b)Ta có: 02006=02
12006=12
(-1)2006=(-1)2
=>x E {-1;'0;1}
a) (x-5)4 = (x-5)6
=>(x-5)4 - (x-5)6=0
=>(x-5)4[1-(x-5)2]=0
=>(x-5)4[1-x2+10x-25]=0
=>(x-5)4[6x-24+4x-x2]=0
=>(x-5)4[6(x-4)-x(x-4)]=0
=>(x-5)4(6-x)(x-4)=0
=>(x-5)4=0 hoặc 6-x=0 hoặc x-=0
=>x=5 hoặc x=6 hoặc x=4
b)x2006=x2
=>x2006-x2=0
=>x2(x2004-1)=0
=>x2=0 hoặc x2004-1=0
=>x=0 hoặc x=1 hoặc -1
\(a.\left(x-5\right)^4=\left(x-5\right)^6\)
\(\Leftrightarrow0=\left(x-5\right)^6-\left(x-5\right)^4\)
\(\Leftrightarrow\left(x-5\right)^4.\left[\left(x-5\right)^2-1\right]=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(x-5\right)^4=0\\\left(x-5\right)^2-1=0\end{cases}}\) \(\Leftrightarrow\orbr{\begin{cases}x-5=0\\x-5=1;-1\end{cases}}\) \(\orbr{\begin{cases}x-5=0\\\orbr{\begin{cases}x-5=1\\x-5=-1\end{cases}}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0+5=5\\\orbr{\begin{cases}x=1+5=6\\x=\left(-1\right)+5=4\end{cases}}\end{cases}}\)
