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what is muirheads' inequality?
Try a = 2, b = 2, c = 1.
You are okay after A)
Mistake made in B.
It was a pretty good idea though.
It is okay. I am not sure about the problem either.
Ok, my mistake.
Not if you have
This is for grade 9 and the other two were fairly straight forward. Could the question be:
By Muirheads inequality:
Therefore it is not mandatory that this can be done by the AMGM.
So put these together and you get what you wanted.
Now for (3). edit: Many hours later. I cannot do this one yet. I've put out a general request for more brains.
but we know from the case that m and 1 + m > 0 so
Now consider the alternative case that m < 0
That means we can replace |m| with -m
this time we know 1 - m > 0 as m < 0 so
If a product is negative then one factor must be + and one must be - so
either m > 0 and (m + 1) < 0 but this contradicts the assumption that m < 0
or m < 0 and (m + 1) > 0 which leads to -1 < m < 0
Now to look at number (2). See next post.
Hope that helps