Question

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

Answer 1

Let the numbers be ‘a’ and ‘b’. 

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

⇒ a² – b² = 180 

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

⇒ b² = 8a 

Thus, a² – 8a – 180 = 0

⇒ a² – 18a + 10a – 180 = 0 

⇒ a(a – 18) + 10(a – 18) = 0 

⇒ (a + 10)(a – 18) = 0 

⇒ a = -10, 18 

Thus, the other number is 324 – 180 = b² 

⇒ b = 12 

Numbers are 12, 18 or -12, 18