Question

The sum of the square of 2 positive integers is 208. If the square of larger number is 18 times the smaller number, find the numbers.

Answer 1

Let these two numbers be X and Y, Y being the bigger number. Then as per the question, 

X²+Y²= 208 ..... (i) 

Y² = 18X ..... (ii) 

From (i), we get Y²= 208 - X². Putting this in (ii), we get 

208 - X² = 18X 

⇒ x² + 18X - 208 = 0 

⇒ X² + 26X - 8X - 208 = 0 

⇒ X(X + 26) - 8(X + 26) = 0 

⇒ (X-8) (X+ 26) = 0 

⇒ X can't be a negative number , hence X=8 

⇒ Putting X=8 in (ii), we get Y² = 18 x 8=144 

⇒ Y= l 2

⇒ X=8 and Y = 12.