Question

The value of X obtained on solving the following equations m/x-n/y=a,and m/x+n/y=b is

Answer 1

Therefore $x=\frac{2m}{a+b}$

Step-by-step explanation:

$\frac{m}{x} -\frac{n}{y}=a$.......(1)

$\frac{m}{x} +\frac{n}{y}=b$........(2)

Let $\frac{1}{x} = u$ and $\frac{1}{y} =v$

Then equation (1) and (2) become

mu-nv=a...........(3)

mu+nv=b...........(4)

Equation (3)+ equation(4)

mu - nv+mu +nv=a+b

⇔2mu = a+b

⇔$u = \frac{a+b}{2m}$

$\Leftrightarrow \frac{1}{x} =\frac{a+b}{2m}$

$\Leftrightarrow x=\frac{2m}{a+b}$

Therefore $x=\frac{2m}{a+b}$