Answer :
Given: The sum of the squares of two numbers is 233 and one of the numbers is 3 less than twice the other number.
To find: the numbers.
Solution:
Let one of the numbers 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
According to given condition, a2 + (2a – 3)2 = 233
Apply the formula (x –y )2 = x2 + y2 -2xy on (2a – 3)2
⇒ a2 + 4a2 + 9 – 12a = 233
⇒ a2 + 4a2 + 9 – 12a - 233 = 0
⇒ 5a2 – 12a – 224 = 0
⇒ 5a2 – 40a + 28a – 224 = 0
⇒ 5a(a – 8) + 28(a – 8) = 0
⇒ (5a + 28)(a – 8) = 0
⇒ (5a + 28) = 0 and (a – 8) = 0
To satisfy the given conditions a will be 8.
2nd number = 2(8) – 3 = 16-3 = 13
Thus the numbers are 8, 13.
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
view all courses
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation

