Q. 65.0( 3 Votes )

The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.

Answer :

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


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