Yeah, it needs some kind of intuition (and basically bang you head against the wall until you find it lol). Although this one isn't too hard to figure it out.
Here's my thinking process:
The 9 on the LHS looks familiar, isn't it? We've seen that in (b)!
So maybe we want to use that inequality somehow, i.e. replace a,b,c with something else.
If you get confused, maybe try rewriting the second inequality in (b) with x,y,z instead of a,b,c, and then replace the x,y,z with something.
Solution, albeit a _very_ short one:
https://www.docdroid.net/KqcrGNC/ineq-pdf
Note: Beware! Your work doesn't end here.
Mild de-brief: I think inequality problems are just hard because "it needs intuition", but I think often times the proof will work itself out when you (i) work backwards; and (ii) review what you are given/proved, and spot similarities. If you look at HKALE Pure Math inequality problems, the substitutions are wild, but often times you can work it out just by doing the two things I've mentioned.
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本帖最後由 風之男 於 2022-4-3 08:57 PM 編輯 ]
