Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 4 of Exercise 10E
Listen NCERT Audio Books to boost your productivity and retention power by 2X.
The sum of the squares of two consecutive positive integers is 365. Find the integers.
Let the required two consecutive positive integers be x and x + 1
According to given condition,
x2 + (x + 1)2 = 365
x2 + x2 + 2x + 1 = 365 using (a + b)2 = a2 + 2ab + b2
2x2 + 2x – 364 = 0
x2 + x – 182 = 0
Using the splitting middle term – the middle term of the general equation 
is divided in two such values that:
Product = a.c
For the given equation a = 1 b = 1 c = – 182
= 1. – 182 = – 182
And either of their sum or difference = b
= 1
Thus the two terms are 14 and – 13
Difference = 14 – 13 = 1
Product = 14. – 13 = – 182
x2 + x – 182 = 0
x2 + 14x – 13x – 182 = 0
x(x + 14) – 13(x + 14) = 0
(x + 14) (x – 13) = 0
(x + 14) = 0 or (x – 13) = 0
x = – 14 or x = 13
x = 13 (x is a positive integer)
x + 1 = 13 + 1 = 14
Thus the required two consecutive positive integers are 13, 14
minutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which each pipe would fill the cistern.
