+688 Let $x \mathbin{\spadesuit} y = \frac{x^2}{y}$ for all $x$ and $y$ such that $y\neq 0$. Find all values of $a$ such that $a \mathbin{\spadesuit} (a + 1) = 9$. Write your answer as a list separated by commas.
+129849 \( x \mathbin{\spadesuit} y = \frac{x^2}{y} \)
Find a such that \(a \mathbin{\spadesuit} (a + 1) = 9\)
a^ 2 / ( a + 1) = 9
a^2 = 9 (a + 1)
a^2 = 9a + 9
a^2 - 9a = 9 complete the square on a
a^2 - 9a + 81/4 = 9 + 81/4
(a - 9/2)^2 = 117/4 take both roots
a - 9/2 = sqrt (117) /2 a - 9/2 = -sqrt (117) / 2
a = (9 + 3sqrt (13)) / 2 a = (9 - 3sqrt (13)) / 2
