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

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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, \(a=-9,9.\)

.DanielCai Jul 14, 2018