Question

find the positive integers m, n,p such that 1/m+1/n+1/p = 3/17​

Answer 1

Answer:

m = n = p = 17

Step-by-step explanation:

Since, if,

$\frac{1}{m}+\frac{1}{n}+\frac{1}{p}=\frac{3}{17}$

Then,

LCM(m, n, p) = 17 must be true,

Since factors of 17 = 1, 17,

So, the possible values of m, n and p,

{(1, 1, 17), (1, 17, 17), (17, 17, 17)},

Now, $\frac{1}{1}+\frac{1}{1}+\frac{1}{17}\neq \frac{3}{17}$

$\frac{1}{1}+\frac{1}{17}+\frac{1}{17}\neq \frac{3}{17}$

$\frac{1}{17}+\frac{1}{17}+\frac{1}{17}=\frac{3}{17}$

Hence, the possible values of m, n and p are 17, 17 and 17.

Note : even, If we suppose m, n and p are,

{(-1, 1, 17), (-1, -1, 17), (-1, -1, -17) (-1, 17, 17), (-1, -17, 17), (-1, -17, -17)(-17, 17, 17),(-17, -17, 17), (-17, -17, -17)},

Then we can not get,

$\frac{1}{m}+\frac{1}{n}+\frac{1}{p}=\frac{3}{17}$