\(\left\{{}\begin{matrix}3^x=441\Rightarrow3=441^{\left(\dfrac{1}{x}\right)}\\7^y=441\Rightarrow7=441^{\left(\dfrac{1}{y}\right)}\end{matrix}\right.\)
\(\Rightarrow3.7=441^{\left(\dfrac{1}{x}\right)}.441^{\left(\dfrac{1}{y}\right)}\)
\(\Rightarrow21=441^{\left(\dfrac{1}{x}+\dfrac{1}{y}\right)}=21^{2\left(\dfrac{1}{x}+\dfrac{1}{y}\right)}\)
\(\Rightarrow2\left(\dfrac{1}{x}+\dfrac{1}{y}\right)=1\)
\(\Rightarrow2\left(\dfrac{x+y}{xy}\right)=1\)
\(\Rightarrow\dfrac{xy}{x+y}=2\)
\(\Rightarrow\left(\dfrac{xy}{x+y}\right)^2=4\)
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