Question

Convert the following equation into simultaneous equation and solve.
√x/y=4, 1/x+1/y=1/xy

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Answer 1

The value of x =   $\frac{16}{17}$

The value of y =  $\frac{1}{17}$

Given:

$\sqrt{\frac{x}{y} }$= 4

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

To find:

The conversion of the following equations in two simultaneous equations and solving it.

Explanation:

  $\sqrt{\frac{x}{y} }$= 4      .......................1

  $\frac{1}{x}$ + $\frac{1}{y}$ = $\frac{1}{xy}$ .....................2

Squaring the equation (1), we get  

 $\sqrt{\frac{x}{y} }$ = 4      .....................1

$\frac{x}{y}$ = 4²

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

x = 16y

From equation (2),

  $\frac{1}{x}$ + $\frac{1}{y}$ = $\frac{1}{xy}$    ..................2

$\frac{x+y}{xy}$ =  $\frac{1}{xy}$  

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

x+y = 1    

From the equation (1) ⇒  x = 16y

Substituting the value of x in equation (2), we get

x + y = 1

16y + y = 1

17y = 1

y =    $\frac{1}{17}$

x = $\frac{16}{17}$ y ⇒   $\frac{1}{17}$  

Hence,

The value of x = $\frac{16}{17}$   and value of y =  $\frac{1}{17}$    

To learn more...

1. In Figure-8, ABCD is a parallelogram. A semicircle with centre 0 and the diameter AB has been drawn and it passes through D. If AB = 12 cm and OD 1 AB, then find the area of the shaded region. (Use a = 3-14).

brainly.in/question/15924611

2. Why do we reduce the expression with the help of boolean algebra and demorgan's theorem.

brainly.in/question/11506128

Answer 2

Ans

x=16y............(1)and x+y=1.......2

(x, y)=(16/17,1/17) is the solution