Question

`f) (x^2 – 9)^2 – 9(x – 3)^2 = 0`

Giải pt

Answer 1

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

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

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

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

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

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

\(\Rightarrow\left\{{}\begin{matrix}x=0\\\left(x-3\right)^2=0\\x-6=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\x=3\\x=6\end{matrix}\right.\)

Vậy pt f(x) có tập nghiệm \(f\left(x\right)\in\left\{0;3;6\right\}\)

Answer 2

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

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

hay \(x\in\left\{0;3;-6\right\}\)