Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 6 of Exercise 10E
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The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.
Let the two consecutive positive even numbers be x and (x + 2)
According to given condition,
x2 + (x + 2)2 = 452
x2 + x2 + 4x + 4 = 452 using (a + b)2 = a2 + 2ab + b2
2x2 + 4x – 448 = 0
x2 + 2x – 224 = 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 = 2 c = – 224
= 1. – 224 = – 224
And either of their sum or difference = b
= 2
Thus the two terms are 16 and – 14
Difference = 16 – 14 = 2
Product = 16. – 14 = – 224
x2 + 2x – 224 = 0
x2 + 16x – 14x – 224 = 0
x(x + 16) – 14(x + 16) = 0
(x + 16) (x – 14) = 0
(x + 16) = 0 or (x – 14) = 0
x = – 16 or x = 14
x = 14 (x is positive odd number)
x + 2 = 14 + 2 = 16
Thus the two consecutive positive even numbers are 14 and 16
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.
