Question

tim x biet (x-1)^4 :3^2=3^6

Answer 1

\(\left(x-1\right)^4:3^2=3^6\)

\(\left(x-1\right)^4=3^6.3^2\)

\(\left(x-1\right)^4=3^8\)

\(\left(x-1\right)^4=3^{2.4}=\left(3^2\right)^4=9^4\)

\(\Rightarrow\orbr{\begin{cases}x-1=9\\x-1=-9\end{cases}\Rightarrow\orbr{\begin{cases}x=9+1=10\\x=-9+1=-8\end{cases}}}\)

Vậy: \(\orbr{\begin{cases}x=10\\x=-8\end{cases}}\)

Answer 2

( x - 1 )⁴ : 3² = 3⁶

( x - 1 )⁴ = 3⁶ . 3²

( x - 1 )⁴ = 3⁸

( x - 1 )⁴ = 6561

( x - 1 )⁴ = 9⁴

x - 1 = 9

x = 10

Answer 3

\((x-1)^4:3^2=3^6\)

\(\Rightarrow(x-1)^4=3^6.3^2\)

\(\Rightarrow(x-1)^4=3^8\)

\(\Rightarrow(x-1)^4=3^{2.4}=(3^2)^4=9^4\)

Xét cả hai trường hợp :

\(\hept{\begin{cases}x-1=9\\x-1=-9\end{cases}\Rightarrow}\hept{\begin{cases}x=10\\x=-8\end{cases}}\)

Vậy : \(x\in\left\{10;-8\right\}\)