Question

√x/y=4, 1/x+1/y=1/xy ​

Answer 1

Answer:I think x=16/17and y=1/17

Step-by-step explanation:

Root x/root y =4

x/y=16------by squaring-------

x=16y

x-16y=0----------eq.1

1/x+1/y=1/xy

y+x/xy=1/xy--------cross multiply

x+y=1---------dividing by xy---eq2

By subtracting eq 1and2,we get x=16/17andy=1/17

Answer 2

Given:

$\sqrt{\dfrac{x}{y}} =4$                      ........... (1)

and $\dfrac{1}{x} +\dfrac{1}{y} =\dfrac{1}{xy}$        ........... (2)

We have, to find the values of x and y = ?

Solution:

Squaring both sides in equation (1), we get

$(\sqrt{\dfrac{x}{y}})^2 =4^2$  

⇒ $\dfrac{x}{y}=16$

⇒ x = 16y                    ........... (3)

∴ $\dfrac{1}{x} +\dfrac{1}{y} =\dfrac{1}{xy}$  

⇒ $\dfrac{x+y}{xy}=\dfrac{1}{xy}$  

⇒ x + y = 1               ........... (4)  

From equations (3) and (4), we get

16y + y = 1  

⇒ 17y = 1  

⇒  y = $\dfrac{1}{17}$  

Put y = $\dfrac{1}{17}$   in equation (4), we get

x + $\dfrac{1}{17}$ = 1        

⇒ x = 1 - $\dfrac{1}{17}$

⇒ x = $\dfrac{16}{17}$

Thus, x = $\dfrac{16}{17}$ and  y = $\dfrac{1}{17}$