3x²-51 = 24

=>3x²=75

=>x²=25

=> x = + - 5

\(\left(3x^2-51\right)^{2n}=\left(-24\right)^{2n}\)

\(3x^2-51=-24\)

\(3x^2=27\)

\(x^2=9\)

\(x^2=3^2=\left(-3\right)^2\)

TH1: x=3

TH2: x=-3

=.= hok tốt!!

(3x²-51)²ⁿ=(-24)²ⁿ\(\Rightarrow\)(51-3x²)²ⁿ=(24)²ⁿ\(\Rightarrow\)(51-3x²)=24

\(\Rightarrow\)51-24=3x²\(\Rightarrow\)27\(\Rightarrow\)x²=3²\(\Rightarrow\)x=3 hoặc x=-3

từ đề bài => 3x^2-51=24

=>3x^2=75

=>x^2=75:3=25

=>x=-5 hoặc x=5

a/ \(\Leftrightarrow3^{2x}:3^2=\left(\frac{1}{3}\right)^5\Rightarrow3^x=\frac{1}{3^5}\Rightarrow3^x.3^5=1\Rightarrow3^{5x}=3^0\)

=> 5x = 0 => x = 0 

\(\left(3x^2-51\right)^{2n}=\left(-24\right)^{2n}\)

\(\Leftrightarrow3x^2-51=-24\)

\(\Leftrightarrow3x^2=27\)

\(\Leftrightarrow x^2=9\)

\(\Leftrightarrow x=\pm3\)

(3x² - 51)²ⁿ = (-24)²ⁿ

=> \(\orbr{\begin{cases}3x^2-51=-24\\3x^2-51=24\end{cases}=>\orbr{\begin{cases}3x^2=27\\3x^2=75\end{cases}}}\) 

=>\(\orbr{\begin{cases}x^2=9\\x^2=25\end{cases}=>}\orbr{\begin{cases}x=3\\x=5\end{cases}}\)

b) Gọi d là ước chung của 2n và 2n + 2. 
Suy ra \(\hept{\begin{cases}2n⋮d\\2n+2⋮d\end{cases}}\).
Vì vậy \(2n+2-2n⋮d\) hay \(2⋮d\).
Vậy d = { 1; 2}.

    Giải :

a ) Ta có :

\(51=3.17\)

\(76=2^2.19\)

\(\RightarrowƯC\left(51;76\right)=1\)

b ) Gọi \(Ư\left(2n,2n+2\right)=d\)

\(\Rightarrow\hept{\begin{cases}2n⋮7\\2n+2⋮7\end{cases}\Rightarrow\left(2n+2\right)-2n⋮d\Rightarrow2⋮d}\)hay \(d\inƯ\left(2\right)\)

Ta có : \(Ư\left(2\right)=\left\{1;2\right\}\)

Vậy \(ƯC\left(2n,2n+2\right)=\left\{1;2\right\}\)