Question

If $\frac{1}{x}+\frac{1}{y}=K$ and $\frac{1}{x}-\frac{1}{y}=K$ then the value of $y$:

• A. $-1$
• B. $0$
• C. $1$
• D. Does not exist

Answer 1

Answer: (D)

Does not exist

Given equations are $\frac{1}{x}+\frac{1}{y}=K$ --- $\left(1\right)$
and $\frac{1}{x}-\frac{1}{y}=K$ --- $\left(2\right)$
Adding the equations, we get $\frac{2}{x}=2K$
$\Rightarrow \frac{1}{x}=K$
Substituting in eqn $\left(1\right)$, we get $K-\frac{1}{y}=K$
$\Rightarrow \frac{1}{y}=0$
$\Rightarrow y=\frac{1}{0}$ which is not defined or does not exist.