Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 1 of Exercise 10E
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1
The sum of a natural number and its square is 156. Find the number.
Let the required number be x
According to given condition,
x + x2 = 156
x2 + x – 156 = 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 = – 156
= 1. – 156 = – 156
And either of their sum or difference = b
= 1
Thus the two terms are 13 and – 12
Sum = 13 – 12 = 1
Product = 13. – 12 = – 156
x2 + x – 156 = 0
x2 + 13x – 12x – 156 = 0
x(x + 13) – 12 (x + 13) = 0
(x – 12) (x + 13) = 0
x = 12 or x = – 13
x cannot be negative
Hence the required natural number is 12
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.
