Math, asked by madhurabondre2017, 11 months ago

xy÷x+y=6÷5 ,xy ÷y-x=6

Answers

Answered by AlluringNightingale
1

Answer:

x = 2 , y = 3

Solution:

The given equations are :

xy/(x + y) = 6/5 -------(1)

xy/(x - y) = 6 -------(2)

Eq-(1) can be rewritten as ;

=> xy/(x + y) = 6/5

{ Reciprocal both the sides }

=> (x + y)/xy = 5/6

{ separate division }

=> x/xy + y/xy = 5/6

=> 1/y + 1/x = 5/6

=> 1/x + 1/y = 5/6 ---------(3)

Eq-(2) can be rewritten as ;

=> xy/(y - x) = 6

{ Reciprocal both the sides }

=> (y - x)/xy = 1/6

{ separate division }

=> y/xy - x/xy = 1/6

=> 1/x - 1/y = 1/6 ---------(4)

Now,

Adding eq-(3) and eq-(4) ,

We get ;

=> 1/x + 1/y + 1/x - 1/y = 5/6 + 1/6

=> 1/x + 1/x = (5+1)/6

=> 2/x = 6/6

=> 2/x = 1

=> x/2 = 1

=> x = 2

Now,

Putting x = 2 in eq-(3) , we get ;

=> 1/x + 1/y = 5/6

=> 1/2 + 1/y = 5/6

=> 1/y = 5/6 - 1/2

=> 1/y = (5 - 3)/6

=> 1/y = 2/6

=> 1/y = 1/3

=> y = 3

Hence,

x = 2 and y = 3

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