Question

deteeminati x si y stiind ca
${x}^{2} + {y}^{2} - 6 \sqrt{3} x + 4 \sqrt{5} y + 47 = 0$
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Answer 1

$x^2+y^2-6\sqrt{3}x+4\sqrt{5}y+47=0\\ \\ x^2-6\sqrt 3x+(3\sqrt 3)^2+y^2+4\sqrt 5 y+(2\sqrt 5)^2 = 0\\ \\ (x-3\sqrt 3)^2+(y+2\sqrt 5)^2 = 0 \\ \\ \Rightarrow x-3\sqrt 3 = 0\quad si\quad y+2\sqrt 5 = 0 \\\\ \Rightarrow \boxed{x = 3\sqrt 3}\quad si\quad \boxed{y = -2\sqrt 5}$