Question

The difference of squares of two numbers is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.

Answer 1

Let the numbers be ‘a’ and ‘b’. 

Given, difference of squares of two numbers is 88. 

⇒ a² – b² = 88 

Also, the larger number is 5 less than twice the smaller number. 

⇒ a = 2b – 5 Thus, (2b – 5)² - b² = 88 

⇒ 4b² + 25 – 20b - b² = 88 

⇒ 3b² – 20b – 63 = 0 

⇒ 3b² – 27b + 7b – 63 = 0 

⇒ 3b(b – 9) + 7(b – 9) = 0 

⇒ (3b + 7)(b – 9) = 0 

⇒ b = 9 

Thus, a = 2 × 9 – 5 = 13