Question

bài 2 : tìm số huu tỉ y biết:

\(\left(3y-1\right)^{10}=\left(3y-1\right)^{20}\)  

bài 3:tìm x biết:

a.\(\left(x-5\right)^2=\left(1-3x\right)^2\)

Answer 1

bài 2 : 

\(\left(3y-1\right)^{10}=\left(3y-1\right)^{20}\)

\(\Rightarrow\left(3y-1\right)^{20}-\left(3y-1\right)^{10}=0\)

\(\Rightarrow\left(3y-1\right)^{10}\left[\left(3y-1\right)^{10}-1\right]=0\)

\(\Rightarrow\orbr{\begin{cases}\left(3y-1\right)^{10}=0\\\left(3y-1\right)^{10}-1=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}3y-1=0\\\left(3y-1\right)^{10}=1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}3y=1\\3y-1=\pm1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}y=\frac{1}{3}\\y=0\text{ }or\text{ }y=\frac{2}{3}\end{cases}}\)

BÀI  3

\(\left(x-5\right)^2=\left(1-3x\right)^2\)

\(\Rightarrow\left(x-5\right)^2-\left(1-3x\right)^2=0\)

\(\Rightarrow\left(x-5-1+3x\right)\left(x-5+1-3x\right)=0\)

\(\Rightarrow\left(4x-6\right)\left(-2x-4\right)=0\)

\(\Rightarrow\orbr{\begin{cases}4x-6=0\\-2x-4=0\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{3}{2}\\x=-2\end{cases}}}\)