Question

find m and n which satisfy the equation 1/m+1/n=1/5​

Answer 1

Explanation:

pairs (49, 588) (51, 204) (57, 76)

We are given that 1/m + 4/n = 1/12 such that n is odd and 0 < n < 60.

Let us try and find out the value of m in terms of n

=> 1/m = 1/12 - 4/n

=> 1/m = (n - 48)/12n

=> m = 12n/(n - 48)

So, we can say that n > 48

Possible odd values of n such that 48 < n < 60 are 49, 51, 53, 55, 57 and 59

n = 49, m = 588

n = 51, m = 204

n = 53, m = non-integral value

n = 55, m = non-integral value

n = 57, m = 76

n = 59, m = non-integral value

There are 3 pairs of positive integers that satisfy the given conditions.

Answer 2

$\frac{1}{m} + \frac{1}{n} = \frac{1}{5} \\ \\ = > \frac{n + m}{mn} = \frac{1}{5} \\ \\ = > \frac{mn}{m + n} = 5 \\ \\ then \: m = 4 \: and \: n = 5 \\ \\ = > \frac{45}{4 + 5} = \frac{45}{9} = 5$