[hệ phương trình] đề thi Olympic 30-4

N

nguyenbahiep1

lấy (1) - (2)

[laTEX]dk: x, y \geq 0 \\ \\ \frac{x^2-y^2+2(x-y)}{\sqrt{x^2+2x+22} + \sqrt{y^2+2y+22}}+\frac{x-y}{\sqrt{x}+\sqrt{y}} = (y+1)^2-(x+1)^2 \\ \\ \\ \frac{(x-y)(x+y+2)}{\sqrt{x^2+2x+22} + \sqrt{y^2+2y+22}}+\frac{x-y}{\sqrt{x}+\sqrt{y}} + (x-y)(x+y+2) = 0 \\ \\ TH_1: x =y \Rightarrow \sqrt{x^2+2x+22}-\sqrt{x} = (x+1)^2 \Rightarrow x = 1 = y \\ \\ TH_2: \frac{x+y+2}{\sqrt{x^2+2x+22} + \sqrt{y^2+2y+22}}+\frac{1}{\sqrt{x}+\sqrt{y}} + x+y+2 = 0 (vo-nghiem-vi-VT > 0 ) [/laTEX]
 
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