Question

giải pt

a> x^2+y^2+2x-4y+5=0

b> x^2+4y^2-x-4y+5/4=0

Answer 1

a) x² + y² +2x - 4y + 5 = 0

( x² + 2x + 1 ) + ( y² - 4y + 4 ) = 0

( x + 1 )² + ( y - 2 )² = 0

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

Answer 2

b) \(x^2+4y^2-x-4y+\dfrac{5}{4}=0\)

\(x^2-x+\dfrac{1}{4}+4y^2-4y+1=0\)

\(\left(x-\dfrac{1}{2}\right)^2+\left(2y-1\right)^2=0\)

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