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