Question

Tìm các số x, y, t biết

x^2+14y^2+t^2+2xy+6yt-12y+9=0

Answer 1

\(x^2+2xy+y^2+9y^2+6yt+t^2+4y^2-12y+9=0\)

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

\(\Leftrightarrow\left\{{}\begin{matrix}x+y=0\\3y+t=0\\2y-3=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}y=\frac{3}{2}\\t=\frac{-9}{2}\\x=\frac{-3}{2}\end{matrix}\right.\)

Answer 2

pt <=> (x² + 2xy + y²) + (t² + 6yt + 9y²) + (4y² - 12y + 9) = 0

<=> (x + y)² + (t + 3y)² + (2y - 3)² = 0

<=> \(\left\{{}\begin{matrix}\left(x+y\right)^2=0\\\left(t+3y\right)^2=0\\\left(2y-3\right)^2=0\end{matrix}\right.\)

<=> \(\left\{{}\begin{matrix}x=-y=-\dfrac{3}{2}\\t=-3y=-\dfrac{9}{2}\\y=\dfrac{3}{2}\end{matrix}\right.\)

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