Question

tìm x biết: (3x-7)²⁰¹⁵=(3x-7)²⁰¹⁷

Answer 1

\(\left(3x-7\right)^{2015}=\left(3x-7\right)^{2017}\Rightarrow\left(3x-7\right)^{2017}-\left(3x-7\right)^{2015}=0\Leftrightarrow\left(3x-7\right)^{2015}\left[\left(3x-7\right)^2-1\right]=0\Leftrightarrow\orbr{\begin{cases}3x-7=0\\\left(3x-7\right)^2=1\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}3x=7\\3x-7=1\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{7}{3}\\x=\frac{1+7}{3}=\frac{8}{3}\end{cases}}\)
Vậy phương trình có hai nghiệm là \(x=\frac{7}{3}\)và \(x=\frac{8}{3}\)

Answer 2

Vì \(\left(3x-7\right)^{2015}=\left(3x-7\right)^{2017}\) =>3x-7=0 hoặc 3x-7=1

Nếu 3x-7=0=>x=\(\frac{7}{3}\)Nếu 3x-7=1=>x=\(\frac{8}{3}\)

Vậy \(x=\orbr{\begin{cases}\frac{7}{3}\\\frac{8}{3}\end{cases}}\)