Question

Convert the following equations into simultaneous equations an
solve
$\sqrt{x \div y } = 4 \\ \frac{1}{x} + \frac{1}{y} = \frac{1}{xy}$
​

Answer 1

ANSWER:-

take √x/y = 4 ......as 1eqn

and take 1/x+ 1/y = 1/xy as 2nd eqn

squaring on both side of eqn 1

x/y = 16

x=16y

x-16y =0 ........( 3 )

solve 2nd eqn

y+x/xy = 1/xy

y+x=1 (multiply by xy on both side.)

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

solve 3 and 4 eqn

x-x - 16 y - y =0 -1

-17y = -1

y = 1/17

put y= 1/17 in 4th eqn

x + 1/17 = 1

17x +1 / 17 = 1

17x +1 = 17

17x = 17- 1

x= 16/17

therefore x = 16/17 and y = 1/17 is the solution of the given simultaneous equation.

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Answer 2

Simplify:

Step-by-step explanation:

$\ Given \ Value:\\\\ \sqrt{x\div y}=4..........(i)\\\\\frac{1}{x}+\frac{1}{y}=\frac{1}{xy}.........(ii)\\\\\ Find: \\\\\ x= ?\\\\\ y= ?\\\\\ Solution: \\\\\ Square \ of \ the \ equation \ (i)\\\\\rightarrow (\sqrt{x\div y})^2=(4)^2\\\\\rightarrow (\frac{x}{y})=16\\\\\rightarrow x=16y..........(iii)$

$\rightarrow \frac{1}{x}+\frac{1}{y}=\frac{1}{xy}\\\\\rightarrow \frac{y+x}{xy}=\frac{1}{xy}\\\\\rightarrow y+x=1\\\\\ put \ the \ value \ of \ x \ in \ below \ equation\\\\ \rightarrow y+16y=1\\\\\rightarrow 17y=1\\\\\rightarrow y=\frac{1}{17}\\\\\ put \ the \ value \ y \ in \ equation \ (iii)\\\\\rightarrow x=16y\\\\\rightarrow x= 16\times\frac{1}{17}\\\\\rightarrow x=\frac{16}{17}$

Learn more:

• Simplify: https://brainly.in/question/8451502