Q. 14.4( 15 Votes )

The sum of a natural number and its square is 156. Find the number.

Answer :

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


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