Q. 285.0( 4 Votes )

The sum of a number and its reciprocal is . Find the number.

Answer :

Let the required number be x.

According to the given condition,




30x2 + 30 = 61x


30x2 – 61x + 30 = 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 = 30 b = – 61 c = 30


= 30.30 = 900


And either of their sum or difference = b


= – 61


Thus the two terms are – 36 and – 25


Sum = – 36 – 25 = – 61


Product = – 36. – 25 = 900


30x2 – 36x – 25x + 30 = 0


6x(5x – 6) – 5(5x – 6) = 0


(5x – 6) (6x – 5) = 0


(5x – 6) = 0 or (6x – 5) = 0



Hence the required number is


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