The difference of the squares of two numbers is $180$. The square of the smaller number is $8$ times the greater number. Find the two numbers.

Question

Accepted Answer

Step 1: Let the two numbers be $x$ and $y$, $x > y$. $x^2 - y^2 = 180$ ... (i)
Step 2: $y^2 = 8x$ ... (ii)
Step 3: Thus $x^2 - 8x - 180 = 0$
Step 4: $\Rightarrow (x - 18)(x + 10) = 0$
Step 5: Therefore, $x = 18$, $y = \pm 12$

Question

Solution