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Let $x\mathbin{\spadesuit}y = x^2/y$ for all $x$ and $y$ such that $y\neq 0$. Find all values of $a$ such that $a\mathbin{\spadesuit} 3 = 9$. List the values you find in increasing order, separated by commas.

Lightning  Jul 14, 2018
 #1
avatar+117 
+1

Let  \(x\mathbin{\spadesuit}y = x^2/y\) for all \(x\) and \(y\) such that \(y\neq 0\). Find all values of \(a\) such that \(a\mathbin{\spadesuit} 3 = 9\). List the values you find in increasing order, separated by commas.

 

 

Since \(a\mathbin{\spadesuit} 3 = 9\), we know that \(\frac{a^2}{3^2}=9\). Simplifying this gives us \(\frac{a^2}{9}=9\). When we multiply by 9 on both sides, we get \(a^2=81\). So, \(a=-9,9.\)

DanielCai  Jul 14, 2018
 #2
avatar+560 
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YOur woring, but thatnks for trying. It's -3\sqrt{3},3\sqrt{3}.

Lightning  Jul 14, 2018
 #3
avatar+7002 
+1

\(a\spadesuit 3 = 9\\\dfrac{a^2}{3} = 9\\a^2 = 27\\a = \pm\sqrt{27} = \pm3\sqrt{3} \)

Which means a = -3sqrt(3) or a = 3sqrt(3)

MaxWong  Jul 15, 2018
edited by MaxWong  Jul 15, 2018

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