Question

under root x/y=4, 1/x+1/y=1/xy​

Answer 1

Step-by-step explanation:

First square the eqn 1

take lcm in 2 equation

then u will get 2 simultaneous equation

solve it

the answer for x will be 16/17

and y will be 1/17

Answer 2

Answer is $x = \frac {16}{17}$ & $y = \frac {1}{17}$

Step-by-step explanation:

$\sqrt {\frac{x}{y}} = 4$ and $\frac {1}{x} + \frac {1}{y} = \frac {1}{xy}$

a.) $\sqrt {\frac{x}{y}} = 4$

Squaring both sides we get -

So, $(\sqrt {\frac{x}{y}})^2 = 4^2$

$\frac {x}{y} = 16$

$x = 16y$

So, x - 16y = 0 """(1)

b.) $\frac {1}{x} + \frac {1}{y} = \frac {1}{xy}$

Taking LCM we get -

$\frac {y}{xy} + \frac {x}{xy} = \frac {1}{xy}$

⇒$\frac {x+y}{xy} = \frac {1}{xy}$

⇒ $x+y = 1$ """(2)

Substituting equation (1) in (2) we get-

$x+y = 1$

⇒ $x-16y = 0$

⇒$17y = 1$  

⇒$y = \frac {1}{17}$

Putting $y = \frac {1}{17}$ in equation (2) we get -  

x+y = 1

so, $x+ \frac {1}{17} = 1$

or $x = 1-\frac {1}{17}$

⇒$x = \frac {17-1}{17}$

⇒$x = \frac {16}{17}$