Inequality

[colakumarfanta]

if x is not equal to y, is xy =- 1?
1) x +1 / y = y +1 / x
2) (x + y) ^ 2 = x ^ 2 + y ^ 2-2

[mchaubey]

Simplifying S2:

x^2+ y^2 + 2xy= x^2+ y^2 -2
thus 2xy= -2
therefor xy=-1

Sufficient

(x+1)/y= (y+1)/x
=>x(x+1)= y(y+1)
=>x^2+x= y^2+y

Not Suff.

Thus B

[scoobydooby]

would go with D

1) x +1 / y = y +1 / x
=>x-y=1/x - 1/y
=>x-y=(y-x)/xy
=>x-y= -(x-y)/xy
=>xy=-1

hence statement 1 is sufficient as well

[debmalya_dutta]

each statement individually sufficient to answer
option D

2nd statement -> (x+y)^2=x^2+y^2-2

2XY+2=0 => XY=-1

1st statement
x+1/y=y+1/x
=> (xy+1)(1/y-1/x)=0 so either xy=-1 or from the second piece x=y which is not the case as mentioned in the question .
So solution is xy=-1