If `5x(1+ 1/(x^(2)+y^(2)))=12` and `5y(1- 1/(x^(2)+y^(2)))=4 AAx,yepsilonR`, then correct option is/are

Options

A. `|x|=|y|=3`
B. `x+y=1/5`
C. `|x|+|y|=3/5`
D. `x^(2)+y^(2)=5`

Answer

B, C, D

Explanation

`x=12/15 xx 1/ ((1+1/ (x^(2)+y^(2)))`………(i)
and `y=4/5 xx (1/(1- 1/(x^(2)+y^(2))))`………(ii)
Put `x^(2)+y^(2)=1/u` and add `(i)^(2)` and `(ii)^(2)`
`implies1/u=(4/5)^(2) (9/((1+4)^(2))+1/((1-4)^(2)))`
`implies 25(u^(2)-2+1/(u^(2)))=32 {5 (4+ 1/4)-8}`
Put `u+1/u=vimpliesv=6/5` or `26/5`
`implies4=5` or `1/5`
`implies(x,y)=(2,1)` or `(2/5, (-1)/5)`