Symmetric reasoning
Can you sum up the solutions to this equation?
Age
14 to 16
Challenge level
Problem
Find the sum of all the solutions of the equation $6x = \frac{150}{x}$
This problem is taken from the UKMT Mathematical Challenges.
Student Solutions
Answer: $0$
$\begin{align} 6x=\frac{150}x&\Rightarrow6x^2=150\\
&\Rightarrow x^2=25\\
&\Rightarrow x=5\text{ or }x=-5\\
&\quad\qquad5+-5=0\end{align}$