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The operation * is defined for non-zero a and b as follows: a*b = a^2 + b^2.  If a+b = 13 and  ab = 25, what is the value of a*b? Express your answer as a common fraction.

 May 3, 2022
 #1
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Note that \(a \star b\) really looks like \((a + b)^2\), but it is not actually that, so we work around that by doing this:

 

\(a\star b = a^2 + b^2 = (a^2 \color{red} + 2ab\color{black} + b^2) \color{red} - 2ab\color{black} = (a + b)^2 - 2ab\)

 

Now, use a + b = 13 and ab = 25, you will get \(a \star b = 119\). Please tell me if you encounter any difficulty in the calculation.

 May 3, 2022

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