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If $a \clubsuit b = a^2 - 2ab + b^2$ and $2 \clubsuit x = 81$, find the sum of all possible values of x.

 Apr 7, 2021
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$a^2-2ab+b^2=(a-b)^2$

 

So $(2-x)^2=81\implies 2-x=\pm 9$. If $2-x=9, x=-7$. If $2-x=-9, x=11$.

 

Sum is $11-7=4$.

 Apr 7, 2021

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