Ta có:
\(\left(x-5\right)^4=\left(x-5\right)^6\)
\(\Rightarrow\left(x-5\right)^6-\left(x-5\right)^4=0\)
\(\Rightarrow\left(x-5\right)^4.\left[\left(x-5\right)^2-1\right]=0\)
\(\Rightarrow\left(x-5\right)^4=0\) hoặc \(\left(x-5\right)^2+1=0\)
TH1: (x-5)4=0=> x-5=0=> x=5
TH2: (x-5)2+1=0
=> (x-5)2=1
=>x-5=1 hoặc -1
=> x=6 hoặc 4
(x-5)^4=(x-5)^6
(x-5)^4=(x-5)^4.(x-5)^2
=>(x-5)^2=(x^5):(x-5)^4
=>(x-5)^2=1^2
=>x-5=1
=>x=6
Vậy x=6