Question

if x+1/x = 7 and y-1/y =4 then xy+1/xy =?​

Answer 1

Answer:

What is the value of x and y if x+y=1-xy and 7(x-y) =1+xy?

x + y = 1 - xy……………..(1)

7x-7y = 1 + xy… …………….(2)

By adding eq(1) & (2(

8x - 6 y = 2

or 4x - 3y = 1

or x=(1+3y)/4…………….(3)

x+y = 1 - xy……………..(1)

x + xy = 1 - y

x (1 + y ) = (1 - y )

On putting x =(1+3y)/4 from eq. (3)

1/4. (1 + 3 y)×( 1 + y ) = (1 - y )

or 1 + 4y + 3y ^2 = 4 - 4y

or 3y^2 +8y -3 =0

or 3y^2+9y-y-3=0

or 3y(y+3) -1(y+3)=0

or (y+3) (3y-1)=0

y = -3 , 1/3

But x =(1+3y)/4

x= (1–9)/4 , (1+3.1/3)/4

x = -2 , 1/2

Answer:-

x = -2 , 1/2

y = -3 , 1/3