Question

Solve:? `5x (1 + 1/(x^2 + y^2)) = 12` and `5y (1 - 1/(x^2 + y^2)) = 4`

Answer 1

See the answer below...

Explanation:

`5x(1+1/(x^2+y^2))=12` `color(red)" | "` `5y(1-1/(x^2+y^2))=4`
`=>(1+1/(x^2+y^2))=12/(5x)` `color(red)" |"` `=>(1-1/(x^2+y^2))=4/(5y)`

From both equation,

`color(red)(12/(5x)+4/(5y)=2`
`=>12/(5x)=2-4/(5y)`
`=>6/(5x)=1-2/(5y)`
`=>(5x)/6=(5y)/(5y-2)`
`=>x=(6y)/(5y-2)`

Putting it in first equation,
`color(green)(5cdot(6y)/(5y-2){1+1/(y^2+((6y)/(5y-2))^2)}=12`

Help me now.

Answer 2

See below.

Explanation:

`x^2+y^2 = (5x)/(12-5x)`
`x^2+y^2=(5y)/(4-5y)`

now

`(5x)/(12-5x) = (5y)/(4-5y) rArr x = 3y` then

`(3y)^2+y^2 = (5y)/(4-5y) rArr 10y = 5/(4-5y)`

`y = {(1/10(4-sqrt6)),(1/10(4+sqrt6)):}`

`x = {(1/30(4-sqrt6)),(1/30(4+sqrt6)):}`