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Sam
Sum of two numbers is $18$. Sum of their reciprocals is $\dfrac{1}{4}$. Find the numbers.
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jiju
$12$ and $6$
Let numbers be $x$ and $18-x$
$\dfrac{1}{x}+\dfrac{1}{18-x}=\dfrac{1}{4}\\ 4(18-x)+4x=x(18-x)\\ 72-4x+4x=18x-x^2\\ x^2-18x+72=0\\ (x-12)(x-6)=0\\ x=12\text{ or }6$
Numbers are $12$ and $18-12=6$