Is x^2 + y^2 > 6?

1) (x + y)^2 > 6
2) xy = 2


I think plugging in the "numbers" can help us to come a conclusion

Case 1" Let X=2, Y =1
Using those values of X & Y

2^2 +1^2>6
--->5>6

Inference : NO

Case 2:

Let X=5 y= 2/5

Plugging the values,

5^2 +(2/5)^2>6

25.---->6

Inference :YES

Since our plugging of values didn't give a "strong" one sided answer...We can conclude its E

1. (x+y)^2 > 6

x^2 + y^2 + 2xy > 6

From this, we cannot confirm whether x^2 + y^2 > 6. Insufficient.

2. xy = 2
Insufficient.

Combined,
x^2 + y^2 + 2xy > 6 from I
Sub xy=2,
x^2 + y^2 + 2(2) > 6
x^2 + y^2 > 2.
It could be b/w 2 and 6 or greater than 6.
Hence insufficient.

Question is: Is x^2 + y^2 > 6

1) (x+y)^2 > 6
=> x^2 + y^2 + 2xy > 6

Above is NOT SUFFICIENT since we do not know anything about xy.

2) xy=2

Above is NOT SUFFICIENT because, we cannot solve x^2 + y^2 from xy.

Combining 1) and 2), we have x^2 + y^2 > 2

=> x^2 + y^2 can be greather than 2 and less than or equal to 6 or greather than 6. Still INSUFFICIENT.

Hence E.