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.
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