Question

The sum of the square of two numbers is 233. If one of the numbers is 3 less than twice the other number. Find the numbers.

Answer 1

Let the numbers be x, 2x - 3. Then, 

x² + (2x-3)² = 233 

⇒ x² + 4x² + 9 - 12x = 233 

⇒ 5 x² -12x - 224 = 0 

⇒ 5 x² - 40x + 28x - 224 = 0 

⇒ 5x (x - 8) + 28(x - 8) = 0 

⇒ (5x + 28)(x - 8) = 0 

⇒ x = 8  (As the number have to be natural number) 

⇒ Other number = 2 x 8 - 3 =13 

Hence, the numbers are 8 and 13