+0

nonnegative m, n

0
85
2

nonnegative m, n

1/m + 1/n = 2^2/(mn^2)

Jan 12, 2022

#1
+675
0

$$\frac{1}{m} + \frac{1}{n} = \frac{2^2}{(mn^2)}$$ whereby m and n are positive integers and $$m \neq 0$$ and $$n \neq 0$$.

So when m and n are positive then $$n(m + n) = 4$$.

Distribute $$n^2 + nm = 4$$.

There is only one solution: m = 3 and n = 1.

Jan 12, 2022
#2
0

thanks

Jan 12, 2022