Question

\(\left(3x+y\right)^2-3\left(9x^2-y^2\right)-10\left(3x-y\right)^2=0\)

Answer 1

Đặt \(\left\{{}\begin{matrix}3x+y=a\\3x-y=b\end{matrix}\right.\)

\(\Rightarrow a^2-3ab-10b^2=0\)

\(\Leftrightarrow a^2+2ab-5ab-10b^2=0\)

\(\Leftrightarrow a\left(a+2b\right)-5b\left(a+2b\right)=0\)

\(\Leftrightarrow\left(a-5b\right)\left(a+2b\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}a-5b=0\\a+2b=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}3x+y-5\left(3x-y\right)=0\\3x+y+2\left(3x-y\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}-12x+6y=0\\9x-y=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\frac{y}{2}\\x=\frac{y}{9}\end{matrix}\right.\)

Answer 2

Đề bài yêu cầu làm gì vậy bạn?