Question

tìm số hữu tỉ y biết

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

Answer 1

Lời giải:

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

\(\Leftrightarrow (3y-1)^{20}-(3y-1)^{10}=0\)

\(\Leftrightarrow (3y-1)^{10}.(3y-1)^{10}-(3y-1)^{10}=0\)

\(\Leftrightarrow (3y-1)^{10}[(3y-1)^{10}-1]=0\)

\(\Rightarrow \left[\begin{matrix} (3y-1)^2=0\\ (3y-1)^{10}=1\end{matrix}\right.\)

\(\Rightarrow \left[\begin{matrix} 3y-1=0\\ 3y-1=1\\ 3y-1=-1\end{matrix}\right.\Rightarrow \left[\begin{matrix} y=\frac{1}{3}\\ y=\frac{2}{3}\\ y=0\end{matrix}\right.\)

Answer 2

(3y - 1)² = 3y - 1

(3y - 1) (3y - 1) = (3y - 1).1

=> 3y - 1= 1

=> 3y = 2

=> y = \(\)^{\(\dfrac{2}{3}\)}