(Toán 9) Tính gt bt

L

lp_qt

$\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{2014}$

\Leftrightarrow $2014(x+y)=xy$

$P=\dfrac{\sqrt{x+y}}{\sqrt{x-2014}+\sqrt{y-2014}}$

\Rightarrow $P^{2}=\dfrac{x+y}{x+y-2.2014+2.\sqrt{xy-2014(x+y)+2014^{2}}}=\dfrac{x+y}{x+y}=1$
\Rightarrow $P=1$
 
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