RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 10. Quadratic Equations

Subject: Maths - Class 10th

Q. No. 5 of Exercise 10E

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5

The sum of the squares of two consecutive positive odd numbers is 514. Find the numbers.

Let the two consecutive positive odd numbers be x and x + 2

According to given condition,


x2 + (x + 2)2 = 514


x2 + x2 + 4x + 4 = 514 using (a + b)2 = a2 + 2ab + b2


2x2 + 4x – 510 = 0


x2 + 2x – 255 = 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 = – 255


= 1. – 255 = – 255


And either of their sum or difference = b


= 2


Thus the two terms are 17 and – 15


Difference = 17 – 15 = 2


Product = 17. – 15 = – 255


x2 + 2x – 255 = 0


x2 + 17x – 15x – 255 = 0


x(x + 17) – 15(x + 17) = 0


(x + 17) (x – 15) = 0


(x + 17) = 0 or (x – 15) = 0


x = – 17 or x = 15


x = 15 (x is positive odd number)


x + 2 = 15 + 2 = 17


Thus the two consecutive positive odd numbers are 15 and 17


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