Question

Tìm x,y thỏa mãn 3x²+y²+2x-2y-1=0 và 2x(x+y)=2 ai tich x,y hộ mik với

 

Answer 1

\(3x^2+y^2+2x-2y-1=0\)

\(\Leftrightarrow x^2+2x\left(x+y\right)-2xy+y^2+2x-2y-1=0\)

\(\Leftrightarrow x^2+2-2xy+y^2+2x-2y-1=0\)

\(\Leftrightarrow\left(x-y\right)^2+2\left(x-y\right)+1=0\)

\(\Leftrightarrow\left(x-y+1\right)^2=0\)

\(\Leftrightarrow x-y+1=0\)

\(\Leftrightarrow y=x+1\)

Thế vào \(x\left(x+y\right)=1\)

\(\Rightarrow x\left(2x+1\right)=1\)

\(\Leftrightarrow2x^2+x-1=0\Rightarrow\left[{}\begin{matrix}x=-1\Rightarrow y=0\\x=\dfrac{1}{2}\Rightarrow y=\dfrac{3}{2}\end{matrix}\right.\)