1/ ĐKXĐ:
\(\Leftrightarrow x^2+2x.\frac{x}{x-1}+\left(\frac{x}{x-1}\right)^2-\frac{2x^2}{x-1}=3\)
\(\Leftrightarrow\left(x+\frac{x}{x-1}\right)^2-\frac{2x^2}{x-1}-3=0\)
\(\Leftrightarrow\left(\frac{x^2}{x-1}\right)^2-\frac{2x^2}{x-1}-3=0\)
Đặt \(\frac{x^2}{x-1}=a\)
\(\Rightarrow a^2-2a-3=0\Rightarrow\left[{}\begin{matrix}a=-1\\a=3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\frac{x^2}{x-1}=-1\\\frac{x^2}{x-1}=3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x^2+x-1=0\\x^2-3x+3=0\end{matrix}\right.\)
2/ Pt dưới tương đương:
\(\left(2x+y\right)^2-2\left(2x+1\right)+1=0\)
\(\Leftrightarrow\left(2x+y-1\right)^2=0\)
\(\Leftrightarrow2x+y-1=0\Rightarrow y=1-2x\)
Thay vào pt trên:
\(x^2+x\left(1-2x\right)+2=0\)
\(\Leftrightarrow-x^2+x+2=0\)
3/ Chắc là \(P=4x^2+9y^2\)
\(15^2=\left(2.2x+3y\right)^2\le\left(2^2+1^2\right)\left(4x^2+9y^2\right)\)
\(\Rightarrow4x^2+9y^2\ge\frac{15^2}{5}=45\)
\(P_{min}=45\) khi \(\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\)
