+0

# Operations

0
26
1

If $a \clubsuit b = a^2 - 2ab + b^2$ and $2 \clubsuit x = 81$, find the sum of all possible values of x.

Apr 7, 2021

#1
+421
+1

$a^2-2ab+b^2=(a-b)^2$

So $(2-x)^2=81\implies 2-x=\pm 9$. If $2-x=9, x=-7$. If $2-x=-9, x=11$.

Sum is $11-7=4$.

Apr 7, 2021