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

Given, difference of the squares of two numbers is 180.

= k² - l² - 180

Also, square of the smaller number is 8 times the larger.

= l² = 8k

Thus, k² - 8a - 180 = 0

k² – 18k + 10k - 180 = 0

→  k(k - 18) + 10(k – 18) = 0

= (k + 10)(k – 18) = 0

→  k = -10, 18

Thus, the other number is

324 - 180 = l² 

→ Numbers are 12, 18 or -12, 18.