+0

# Help!

-1
728
3
+1206

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.

Jul 14, 2018

#1
+147
0

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, $$a=-9,9.$$

.
Jul 14, 2018
#2
+1206
0

YOur woring, but thatnks for trying. It's -3\sqrt{3},3\sqrt{3}.

Lightning  Jul 14, 2018
#3
+7683
+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)

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