Question

2x=3y=6-z, show that 1/x+1/y+1/z=0

Answer 1

Ans.

$2x = 3y = 6 - z \\ or \: 2x = 3y = 6 - z = k(say) \\ or \: x = \frac{k}{2} \\ y = \frac{k}{3} \\ z = 6 - k$

Now,
$\frac{1}{x} + \frac{1}{y} + \frac{1}{z} \\ = \frac{1}{ \frac{k}{2} } + \frac{1}{ \frac{k}{3} } + \frac{1}{6 - k} \\ = \frac{2}{k} + \frac{3}{k} + \frac{1}{6 - k} \\ = \frac{5}{k} + \frac{1}{6 - k}$

I THINK YOUR QUESTION IS WRONG.