Toán Giải hệ phương trình?

C

conga222222

$\eqalign{
& \left\{ \matrix{
x + \sqrt {{x^2} - 2x + 5} = 3y + \sqrt {{y^2} + 4} \cr
{x^2} - {y^2} - 3x + 3y + 1 = 0 \cr} \right. \cr
& dk... \cr
& \to x + \sqrt {{x^2} - 2x + 5} + {x^2} - {y^2} - 3x + 3y + 1 = 3y + \sqrt {{y^2} + 4} \;(1) \cr
& dat\;a = \sqrt {{x^2} - 2x + 5} ;\;b = \sqrt {{y^2} + 4} \;\left( {a \ge 2;\;b \ge 2} \right) \cr
& \to \left( 1 \right) \leftrightarrow {a^2} + a = {b^2} + b \cr
& xet\;f(t) = {t^2} + t \cr
& \to {f^/}(t) = 2t + 1 > 0\;\forall t \ge 2 \cr
& \to {f^/}(t)\;dong\;bien \cr
& \to (1) \leftrightarrow a = b \to \sqrt {{x^2} - 2x + 5} = \sqrt {{y^2} + 4} \cr
& \to ... \cr} $
 
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