Two distinct numbers $ a $ and $ b $ are selected from $ 1,2,3, \ldots, 60 . $ Find the maximum value of the fraction $ \frac{a \times b}{a-b} $
Given: Two distinct numbers a and b are selected from 1,2,3, ...... 60 .
To do: Find the max value of the fraction $\frac{a \times b}{a - b}$
Solution:
To make the fraction $\frac{a \times b}{a - b}$ have maximum value, the numerator should have maximum value and the denominator should have the minimum value.
The numerator a x b is maximum if a = 60 and b = 59.
The denominator ( a - b) is minimum if a and b are consecutive numbers.
If a = 60 and b = 59, the fraction has maximum value
which is = 60 $\times$ 59 = 3540
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