The difference of squares of two numbers is 88. If the larger number i

1.	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» 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

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»

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