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The operation \(*\) is defined for non-zero a andb  as follows: \(a * b = \frac{1}{a} + \frac{1}{b}.\)  If a+b=13 and \(a \times b=25\) , what is the value of \(a*b\)?Express your answer as a common fraction.

ant101  Aug 28, 2018

Best Answer 

 #1
avatar+3270 
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We know that: \(\frac{1}{a}+\frac{1}{b}=a*b\) . If we multiply the denominator by b and a, respectively, we get: \(\frac{1b}{ab}+\frac{1a}{ba}=a*b\) . Suddenly, we go back to the problem, and it says: \(ab=25.\) So, we have:\(\frac{1a}{25}+\frac{1b}{25}=\frac{1a+1b}{25}.\) We also know that \(a+b=13\) , so  \(\frac{1a+1b}{25}=\frac{a+b}{25}=\boxed{\frac{13}{25}}.\)

tertre  Aug 28, 2018
 #1
avatar+3270 
+2
Best Answer

We know that: \(\frac{1}{a}+\frac{1}{b}=a*b\) . If we multiply the denominator by b and a, respectively, we get: \(\frac{1b}{ab}+\frac{1a}{ba}=a*b\) . Suddenly, we go back to the problem, and it says: \(ab=25.\) So, we have:\(\frac{1a}{25}+\frac{1b}{25}=\frac{1a+1b}{25}.\) We also know that \(a+b=13\) , so  \(\frac{1a+1b}{25}=\frac{a+b}{25}=\boxed{\frac{13}{25}}.\)

tertre  Aug 28, 2018
 #2
avatar+20147 
+2

The operation \(*\) is defined for non-zero a andb  as follows: 

\(a * b = \frac{1}{a} + \frac{1}{b}. \)

If \(a+b=13\) and \(a \times b=25\)

what is the value of  \(a*b\)  ?

Express your answer as a common fraction.

 

\(\begin{array}{|rcll|} \hline a+b &=& 13 \\ a\times b &=& 25 \\\\ \dfrac{a+b}{a\times b}&=& \dfrac{13}{25} \\\\ \dfrac{a}{a\times b} + \dfrac{b}{a\times b} &=& \dfrac{13}{25} \\\\ \dfrac{1}{b} + \dfrac{1}{a} &=& \dfrac{13}{25} \\\\ \dfrac{1}{a} + \dfrac{1}{b} &=& \dfrac{13}{25} \quad & | \quad \dfrac{1}{a} + \dfrac{1}{b} = a*b \\\\ \mathbf{a*b} & \mathbf{=} & \mathbf{\dfrac{13}{25}} \\ \hline \end{array}\)

 

laugh

heureka  Aug 28, 2018

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