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The product of two numbers a and b is twice the sum of the numbers. What is the sum of the reciprocals…

We are given \(ab = 2(a+b)\). The sum of the reciprocals is \(\frac{1}{a}+\frac{1}{b}=\frac{a+b}{ab}\), so substituting for \(ab\) gives \[\frac{a+b}{2(a+b)}=\frac{1}{2}.\]…

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The product of two numbers a and b is twice the sum of the numbers. What is the sum of the reciprocals of a and b?

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We are given ab=2(a+b)ab = 2(a+b). The sum of the reciprocals is 1a+1b=a+bab\frac{1}{a}+\frac{1}{b}=\frac{a+b}{ab}, so substituting for abab gives a+b2(a+b)=12.\frac{a+b}{2(a+b)}=\frac{1}{2}. Hence the sum of the reciprocals is one half.

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