The sum of the squares of two numbers is 233 and one of the numbers is 3 less than twice the other number. Find the numbers.
Let one of the number be a.
Given, sum of the squares of two numbers is 233 and one of the numbers is 3 less than twice the other number.
2nd number = 2a – 3
⇒ a2 + (2a – 3)2 = 233
⇒ a2 + 4a2 + 9 – 12a = 233
⇒ 5a2 – 12a – 224 = 0
⇒ 5a2 – 40a + 28a – 224 = 0
⇒ 5a(a – 8) + 28(a – 8) = 0
⇒ (5a + 28)(a – 8) = 0
Thus, a = 8
Numbers are 8, 13