Question

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

Answer 1

Let the large number be x. 

8 times larger number = Square of the srnall number = 8x 

Square of the larger number = x² 

By problem, x² – 8x = 180

⇒ x² – 8x – 180 = 0 

⇒ x² – 18x + 10x – 180 = 0 

⇒ x(x – 18) + 10(x – 18) = 0 

⇒ (x + 10)(x – 18) = 0 

⇒ x + 10 = 0 (or) x – 18 = 0 

⇒ x = -10 (or) x = 18 

If x = 18, then larger number =18; 

(small number)2 = 8 × (+18) = 144 

∴ Small number = √144 = 12 

The numbers are 18, 12 

Note: Discard x = -10.