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805+ (Hard)|   Algebra|   Exponents|      
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Dip050701
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Is x^2 + y^2 > 100? (1) 2xy < 100 (2) (x + y)^2 > 200 29 Dec 2022, 00:29
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IanStewart Can we add an inequality (X+Y)^2>200
(X-Y)^2 >= 0
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Is x^2 + y^2 > 100? (1) 2xy < 100 (2) (x + y)^2 > 200 29 Dec 2022, 07:51
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Dipanjan005
IanStewart Can we add an inequality (X+Y)^2>200
(X-Y)^2 >= 0
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Yes, if you have two inequalities that face the same way, you can always add them, and it doesn't matter if one inequality is a "greater than or equal" inequality. So if you have:

x > 5
y > 2

we can add, to get x + y > 7. If instead you have:

x > 5
y > 2

this is almost the same situation, but even if y = 2, it will still always be true that x + y > 7, so again it's fine to add the inequalities. In the situation where both inequalities are "greater than or equal" inequalities, as here:

x > 5
y > 2

then when we add, we get x + y > 7, because maybe x = 5 and y = 2.
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Is x^2 + y^2 > 100? (1) 2xy < 100 (2) (x + y)^2 > 200 28 Mar 2025, 13:11
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Brilliant trick Bunuel ! Loved it
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