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Find the number of ordered pair of real ...

Find the number of ordered pair of real numbers (x, y) satisfying the equation:
`5x(1+1/(x^(2)+y^(2)))=12 & 5y(1-1/(x^(2) + y^(2))) =4`

A

`|x|=|y|=3`

B

`x+y=1/5`

C

`|x|+|y|=3/5`

D

`x^(2)+y^(2)=5`

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
`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)`
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