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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.

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, $a=-9,9.$

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

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