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\(\left(3x^2-51\right)^{2n}=\left(-24\right)^{2n}\)
\(\Leftrightarrow3x^2-51=-24\)
\(\Leftrightarrow3x^2=27\)
\(\Leftrightarrow x^2=9\)
\(\Leftrightarrow x=\pm3\)
(3x2 - 51)2n = (-24)2n
=> \(\orbr{\begin{cases}3x^2-51=-24\\3x^2-51=24\end{cases}=>\orbr{\begin{cases}3x^2=27\\3x^2=75\end{cases}}}\)
=>\(\orbr{\begin{cases}x^2=9\\x^2=25\end{cases}=>}\orbr{\begin{cases}x=3\\x=5\end{cases}}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(3x^2-51\right)^{2n}=\left(-24\right)^{2n}\)
\(3x^2-51=-24\)
\(3x^2=27\)
\(x^2=9\)
\(x^2=3^2=\left(-3\right)^2\)
TH1: x=3
TH2: x=-3
=.= hok tốt!!
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(x+3\right)^{2n+1}=\left(2x-3\right)^{2n+1}\)
\(\Rightarrow\left(x+3\right)=\left(2x-3\right)\)
\(\Rightarrow x+3=2x-3\)
\(\Rightarrow x+3-2x+3=0\)
\(\Rightarrow-x+6=0\)
\(\Rightarrow x=6\)
Vậy x=6
\(\left(x+3\right)^{2n+1}=\left(2x-3\right)^{2n+1}\)
\(\Rightarrow x+3=2x-3\)
\(x+3-2x+3=0\)
\(\left(x-2x\right)+\left(3+3\right)=0\)
\(-x+6=0\)
\(-x=0-6\)
\(-x=-6\)
\(\Rightarrow x=6\)
Vậy \(x=6\).
![](https://rs.olm.vn/images/avt/0.png?1311)
a: \(\left(3x^2-51\right)^{2n}=\left(-24\right)^{2n}=24^{2n}\)
\(\Leftrightarrow3x^2-51=24\) hoặc 3x2-51=-24
=>3x2=75 hoặc 3x2=27
=>x2=25 hoặc x2=9
hay \(x\in\left\{5;-5;3;-3\right\}\)
b: =>x-3>=0 và x-8<=0
=>3<=x<=8