# Find two consecutive positive integers, sum of whose squares is 365.

To Find: Consecutive integers sum of whose square is 365
Consecutive integers mean that the difference between the integers is of 1
Let the consecutive positive integers be x and x + 1.

Given that x2 + (x + 1)2 = 365

⇒ x2 + x2 + 1 + 2x = 365

⇒ 2x2 + 2x – 364 = 0

⇒  x2 + x – 182 = 0

Now to factorize the above quadratic equation, we need to chose numbers such that their product is 182 and difference is 1

⇒ x2 + 14x – 13x – 182 = 0

⇒ x (x + 14) – 13 (x + 14) = 0

(x+14)(x – 13) = 0

Either x + 14 = 0 or x − 13 = 0, i.e., x = 14 or x = 13

Since the question ask for positive integers, x can only be 13.

x + 1 = 13 + 1 = 14

Therefore, two consecutive positive integers will be 13 and 14.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Knowing the Nature of Roots44 mins
Take a Dip Into Quadratic graphs32 mins
Foundation | Practice Important Questions for Foundation54 mins
Nature of Roots of Quadratic Equations51 mins
Getting Familiar with Nature of Roots of Quadratic Equations51 mins
Understand The Concept of Quadratic Equation45 mins
Champ Quiz | Quadratic Equation33 mins
Balance the Chemical Equations49 mins
Quiz | Lets Solve Imp. Qs of Quadratic Equation43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses