Question

√x/y=4; 1/x+1/y=1/xy. Convert the following equation in two simultaneous equation and solve.

Answer 1

Answer:

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Answer 2

Value of x = $\frac{16}{17}$. 

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

$(\sqrt{\frac{x}{y} }) ^2$ = 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 = $\frac{1}{7}$

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

Hence, the value of x = $\frac{16}{17}$  and value of y = $\frac{1}{17}$ .

To learn more...

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

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