\(a,x^{15}=x\\ \Rightarrow x^{15}-x=0\\ \Rightarrow x\left(x^{14}-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x^{14}-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\left(thoaman\right)\\x=1\left(thoaman\right)\\x=-1\left(loại\right)\end{matrix}\right.\)
\(b,\left(2x+1\right)^3=125\\ \Rightarrow\left(2x+1\right)^3=5^3\\ \Rightarrow2x+1=5\\ \Rightarrow2x=4\\ \Rightarrow x=2\left(thoaman\right)\)
\(c,\left(x-5\right)^4=\left(x-5\right)^6\\ \Rightarrow\left(x-5\right)^4-\left(x-5\right)^6=0\\ \Rightarrow\left(x-5\right)^4\left(1-\left(x-5\right)^2\right)=0\\ \Rightarrow\left[{}\begin{matrix}\left(x-5\right)^4=0\\1-\left(x-5\right)^2=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x-5=0\\x-5=1\\x-5=-1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\\x=6\\x=4\end{matrix}\right.\left(thoaman\right)\)
\(d,x^{10}=x^1\\ \Rightarrow x^{10}-x^1=0\\ \Rightarrow x\left(x^9-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x^9-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\left(thoaman\right)\)
\(e,2^x-15=17\\ \Rightarrow2^x=17+15\\ \Rightarrow2^x=32\\ \Rightarrow2^x=2^5\\ \Rightarrow x=5\left(thoaman\right)\)
\(f,\left(7x-11\right)^3=2^5.5^2+200\\ \Rightarrow\left(7x-11\right)^3=32.25+200\\ \Rightarrow\left(7x-11\right)^3=800+200\\ \Rightarrow\left(7x-11\right)^3=1000\\ \Rightarrow\left(7x-11\right)^3=10^3\\ \Rightarrow7x-11=10\\ \Rightarrow7x=21\\ \Rightarrow x=21:7=3\left(thoaman\right)\)
@seven
a: x^15=x
=>x^15-x=0
=>x(x^14-1)=0
=>x=0 hoặc x^14-1=0
=>x=0 hoặc x^14=1
=>x=0;x=1;x=-1
b: =>2x+1=5
=>2x=4
=>x=2
c: =>(x-5)^4[(x-5)^2-1)]=0
=>(x-5)(x-6)(x-4)=0
=>\(x\in\left\{4;5;6\right\}\)
d: x^10=x
=>x^10-x=0
=>x(x^9-1)=0
=>x=0 hoặc x=1
e: 2^x-15=17
=>2^x=32
=>x=5
f: =>(7x-11)^3=1000
=>7x-11=10
=>7x=21
=>x=3
