[Toán 9] $\sqrt{x-2} +\sqrt{y+2011} +\sqrt{z-2012} = \frac{1}{2} ( x+y+z)$

H

huytrandinh

pt tương đương với
$(\sqrt{x-2}-1)^{2}+(\sqrt{y+2011}-1)^{2}+(\sqrt{z-2012}-1)^{2}=0$
$.(\sqrt{x-2}-1)^{2}\geq 0$
$.(\sqrt{y+2011}-1)^{2}\geq 0$
$.(\sqrt{z-2012}-1)^{2}\geq 0$
$=>(\sqrt{x-2}-1)^{2}+(\sqrt{y+2011}-1)^{2}+(\sqrt{z-2012}-1)^{2}=0$
$<=>.(\sqrt{x-2}-1)^{2}=0$
$.(\sqrt{y+2011}-1)^{2}=0$
$.(\sqrt{z-2012}-1)^{2}=0$
$=>x=3,y=-2010,z=2013$
 
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