Math May JJ No. 4 怎莫作

cmtn

4 DS: r < s?
  1) r + s < 1
  2) r平方 < 2s (E)
  lwei评价意见：同意

How to do it? 例举还是列方程？

simkeechai

from condition #1: r + s < 1, we can set any values for them and the values that will satisfy this condition, like fractions, positive or negative values. for example: r = 1/2 and s = 1/3, or r = -4 and s = 1. these two sets satisfy condition #1, but the r in first set is greater than s, and the r in second set is smaller than s, so, we can't answer the question.

from condition #2: we use the assumptions on condition #1 to test in here.

first set r = 1/2, s = 1/3 => r^2 < 2s => 1/4 < 2/3  (no, r > s)

second set r = -4, s = 1 => r^2 < 2s => 16 > 1  (yes, r < s)

so the key for this question is E

cmtn

thanks

then how can you choose the pair efficiently. I mean how can you decide the range of the number's should be in. (i.e. why one pair is between 0 and 1 as 1/3 and 1/2, while the other pair is 1 and 4)

[此贴子已经被作者于2004-5-24 0:56:27编辑过]

cmtn

why no other reply, is it too simple? but I always spend a long time to deal with this kind of question(不等式, unequality).