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