Question

Tìm x biết:

(4x^2-25)^2-9(2x-5)^2=0

 

Answer 1

\(\left(4x^2-25\right)^2-9\left(2x-5\right)^2=0\)

\(\left[\left(2x-5\right)\left(2x+5\right)\right]^2-9\left(2x-5\right)^2=0\)

\(\left(2x-5\right)^2\left[\left(2x+5\right)^2-9\right]=0\)

\(\Rightarrow\orbr{\begin{cases}\left(2x-5\right)^2=0\\\left(2x+5\right)-9=0\end{cases}}\)

+) \(\left(2x-5\right)^2=0\)

\(\Rightarrow2x-5=0\)

\(\Leftrightarrow x=\frac{5}{2}\)

+) \(\left(2x+5\right)^2-9=0\)

\(\Leftrightarrow\left(2x+5-3\right)\left(2x+5+3\right)=0\)

\(\Leftrightarrow\left(2x+2\right)\left(2x+8\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}2x+2=0\\2x+8=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-1\\x=-4\end{cases}}\)

Vậy ....