Question

\(x^2=x^5\)               \(\left(3y-1\right)^{10}=\left(3y-1\right)^{20}\)                \(\left(x-5\right)^2=\left(1-3x\right)^2\)

\(y^{200}=y\)           \(y^{2008}=y^{2010}\)                

Answer 1

a) \(x^2=x^5\Rightarrow x^2=x^2.x^3\Rightarrow1=x^3\Rightarrow1^3=x^3\Rightarrow x=1\)

b)\(y^{200}=y\Rightarrow y^{199}=1\Rightarrow y=1\)

c) \(\left(3x-1\right)^{10}=\left(3y-1\right)^{20}\Rightarrow1=\left(3y-1\right)^{10}\) 

\(\Rightarrow3y-1=1\) hoặc  \(3y-1=-1\)

\(\Rightarrow3y=2\) hoặc \(3y=0\)

\(\Rightarrow y=\frac{2}{3}\) hoặc y =0

d) \(y^{2008}=y^{2010}\Rightarrow1=y^2\Rightarrow\orbr{\begin{cases}y=-1\\y=1\end{cases}}\)

e) \(\left(x-5\right)^2=\left(1-3x\right)^2\Rightarrow x-5=1-3x\Rightarrow x+3x=1+5\Rightarrow4x=6\Rightarrow x=\frac{6}{4}=\frac{3}{2}\)

Can you k for me ,Nhàn Nguyễn Thị Thanh!