$\sqrt{x+1}+\sqrt{(x+1)(y-2)}+x+5=2y+\sqrt{y-2} (1)$
$\frac{(x-8)(y+1)}{x^{2}-4x+7}=(y-2)(\sqrt{x+1}-3) (2)$
ĐK: [tex]x\geq -1;y\geq 2[/tex]
$pt(1)\iff(\sqrt{x+1}-\sqrt{y-2})+((\sqrt{x+1})^2-\sqrt{(x+1)(y-2)}-2(\sqrt{y-2})^2)=0$
$\iff \sqrt{x+1}-\sqrt{y-2} +(\sqrt{x+1}+2\sqrt{y-2})(\sqrt{x+1}-\sqrt{y-2})=0$
$\iff (\sqrt{x+1}-\sqrt{y-2})(1+\sqrt{x+1}+2\sqrt{y-2})=0$
$\iff \sqrt{x+1}-\sqrt{y-2}=0 \iff y=x+3.$
THay vào pt(2)
$\iff \frac{(x-8)(x+4)}{x^2-4x+7}=(x+1)(\sqrt{x+1}-3)=(x+1)(\frac{x-8}{\sqrt{x+1}+3})$
$\iff (x-8)((\frac{(x+4)}{x^2-4x+7})-(x+1)(\frac{1}{\sqrt{x+1}+3})) =0$
+x=8 (t/m)
+$\frac{(x+4)}{x^2-4x+7})=(x+1)(\frac{1}{\sqrt{x+1}+3})(*)$
$(*)\iff (x+4)(\sqrt{x+1})=x^3-3x^2-5$
$\iff (x+1)(x^2-5x+3)+(x+4)(x-2-\sqrt{x+1})=0$
$\iff (x+1)(x^2-5x+3)+(x+4)(\frac{x^2-5x+3}{x-2+\sqrt{x+1}})=0$
$\iff (x^2-5x+3)(x+1+\frac{x+4}{x-2+\sqrt{x+1}})=0$
$\iff (x^2-5x+3)(\frac{(x+1)\sqrt{x+1}+x^2+2}{x-2+\sqrt{x+1}})=0$
$\iff x^2-5x+3=0$
$...$
..........
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
