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Is x^2 + y^2 > 6?
(1) (x + y)^2 > 6
(2) xy = 2
(1) (x + y)^2 > 6
(2) xy = 2
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1. \((x + y)^2 > 6\text{ }\to\text{ }(x ^2+ y^2)+2xy > 6\)
2xy can be positive or negative.
insuff.
2. xy=2:\((6,\frac13)\)(inequality is true) and \((2,1)\) (inequality is false)
insuff.
1&2. \((x ^2+ y^2)+4 > 6\text{ }\to\text{ }(x ^2+ y^2) > 2\)
insuff.
1. \((x + y)^2 > 6\text{ }\to\text{ }(x ^2+ y^2)+2xy > 6\)
2xy can be positive or negative.
insuff.
2. xy=2:\((6,\frac13)\)(inequality is true) and \((2,1)\) (inequality is false)
insuff.
1&2. \((x ^2+ y^2)+4 > 6\text{ }\to\text{ }(x ^2+ y^2) > 2\)
insuff.
