Q. 25.0( 5 Votes )

The sum of a natural number and its positive square root is 132. Find the number.

Answer :

Let the required number be x

According to given condition,



putting we get




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 = – 132


= 1. – 132 = – 132


And either of their sum or difference = b


= 1


Thus the two terms are 12 and – 11


Difference = 12 – 11 = 1


Product = 12. – 11 = – 132




y(y + 12) – 11(y + 12) = 0


(y + 12) (y – 11) = 0


(y + 12) = 0 or (y – 11) = 0


y = – 12 or y = 11 but y cannot be negative


Thus y = 11


Now


x = y squaring both sides


x = (11)2 = 121


Hence the required number is 121


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