Question

[Lại Đức Thắng]

(y/3-5)^2000=(y/3-5)^2008

làm mãi ko ra, khó quá, nhờ mọi người giúp mik giải nó với

Answer 1

[.]

\(\left(\frac{y}{3}-5\right)^{2000}=\left(\frac{y}{3}-5\right)^{2008}\)

\(\Rightarrow\left(\frac{y}{3}-5\right)^{2008}-\left(\frac{y}{3}-5\right)^{2000}=0\)

\(\left(\frac{y}{2}-5\right)^{2000}\left[\left(\frac{y}{3}-5\right)^8-1\right]=0\)

\(\Rightarrow\orbr{\begin{cases}\left(\frac{y}{3}-5\right)^{2000}=0\\\left(\frac{y}{3}-5\right)^8-1=0\end{cases}}\)

+) \(\left(\frac{y}{3}-5\right)^{2000}=0\Rightarrow\frac{y}{3}-5=0\Rightarrow\frac{y}{3}=5\Rightarrow y=15\)

+) \(\left(\frac{y}{3}-5\right)^8-1=0\)

\(\left(\frac{y}{3}-5\right)^8=1\)

\(\left(\frac{y}{3}-5\right)^8=1^8=\left(-1\right)^8\)

\(\Rightarrow\orbr{\begin{cases}\frac{y}{3}-5=1\\\frac{y}{3}-5=-1\end{cases}}\Rightarrow\orbr{\begin{cases}\frac{y}{3}=6\\\frac{y}{3}=4\end{cases}}\Rightarrow\orbr{\begin{cases}y=18\\y=12\end{cases}}\)

Vậy \(y\in\left\{12;15;18\right\}\).