Ta có:
\(\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{4}\)
\(\Rightarrow\dfrac{x+y}{xy}=\dfrac{1}{4}\)
\(\Rightarrow4\left(x+y\right)=xy\)
\(\Rightarrow xy-4x-4y=0\)
\(\Rightarrow x\left(y-4\right)-\left(4y-16\right)=16\)
\(\Rightarrow x\left(y-4\right)-4\left(y-4\right)=16\)
\(\Rightarrow\left(x-4\right)\left(y-4\right)=16\)
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