Question

\(\left(x^2-9\right)^2-9\left(x-3\right)^2=0\)

Answer 1

\(\left(x^2-9\right)^2-9\left(x-3\right)^2=0\)

\(\Leftrightarrow\left[\left(x-3\right)\left(x+3\right)\right]^2-9\left(x-3\right)^2=0\)

\(\Leftrightarrow\left(x-3\right)^2.\left(x+3\right)^2-9\left(x-3\right)^2=0\)

\(\Leftrightarrow\left(x-3\right)^2.\left[\left(x+3\right)^2-9\right]=0\)

\(\Leftrightarrow\left(x-3\right)^2.x\left(x+6\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=0\\x=-6\end{matrix}\right.\)

Vậy;...

Answer 2

\(\left(x^2-9\right)^2-9.\left(x-3\right)^2=0\)

\(\left(x^2-9\right)^2-\left(3.\left(x-3\right)\right)^2=0\)

\(\left(x^2-9\right)^2-\left(3x-9\right)^2=0\)

\(\left(x^2-9-3x+9\right)\left(x^2-9+3x-9\right)=0\)

\(=>x^2-3x=0=>x\left(x-3\right)=0\)

=>x=0 hoặc x-3=0=>x=3 

hoặc \(x^2+3x-18=0\)

\(x^2+6x-3x-18=0\)\(=>x\left(x+6\right)-3\left(x+6\right)=0\)

\(=>\left(x-3\right)\left(x+6\right)=0\)

=>x-3=0=>x=3

hoặc x+6=0=>x=-6