Question

[Lê Thu Phương Anh]

Tìm x,y biết: 5x² + 5y² + 8xy - 2x + 2y - 2 = 0
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Answer 1

[Min]

\(5x^2+5y^2+8xy-2x+2y+2=0\)

\(\left(4x^2+8xy+4y^2\right)+\left(x^2-2x+1\right)+\left(y^2+2y+1\right)=0\)

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

\(4\left(x+y\right)^2+\left(x-1\right)^2+\left(y+1\right)^2=0\)

Vì      \(\left(x+y\right)^2\ge0;\left(x-1\right)^2\ge0;\left(y+1\right)^2\ge0\)

Để    \(4\left(x+y\right)^2+\left(x-1\right)^2+\left(y+1\right)^2=0\)

\(\Leftrightarrow x+y=0\)

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

\(\Leftrightarrow x-1=0\Rightarrow x=1\)

Vậy    \(x=1; y=-1\)