Question

if
x+y = 2xy
x-y = 4xy

then
y² = ?​

Answer 1

Answer :

y² = 1⁄9

Solution :

• Given : x + y = 2xy ---------(1)

x - y = 4xy ------(2)

• To find : y² = ?

Now ,

Eq-(1) can be rewritten as ;

=> x + y = 2xy

=> (x + y)/xy = 2

=> x/xy + y/xy = 2

=> 1/y + 1/x = 2 ---------(3)

Also ,

Eq-(2) can be rewritten as ;

=> x - y = 4xy

=> (x - y)/xy = 4

=> x/xy - y/xy = 4

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

Now ,

Adding eq-(3) and (4) , we get ;

=> 1/y + 1/x + 1/y - 1/x = 2 + 4

=> 2/y = 6

=> 2/6 = y

=> 1/3 = y

=> y = ⅓

=> y² = (⅓)²

=> y² = 1⁄9

Hence , y² = 1⁄9