Question

Tìm các số thỏa mãn

a) x^2 + y^2 - 6x + 10y + 29 = 0

b) 5x^2 + y^2 - 4x + 2xy + 1 = 0

Giúp mình gấp với tks các bạn nhều

Answer 1

\(x^2-6x+9=-y^2-10y-20.\)

\(\left(x-3\right)^2=-y^2-10y-20\)

\(\left(x-3\right)^2=-y^2-10y-20\)

\(\left(x-3\right)^2=-\left(y^2+2.5y+25\right)+5\)

\(\left(x-3\right)^2=-\left(y+5\right)^2+5\)

\(\hept{\begin{cases}x=3\\y+5=\sqrt{5}\Leftrightarrow y=\sqrt{5}-5\end{cases}}\)

b)

\(\left(4x^2-4x+1\right)=-y^2-x^2-2xy\)

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

\(x=\frac{1}{2}\Leftrightarrow y=-\frac{1}{2}\)