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I need help proving an inequality?
Prove that 2a^3 + 11 > 9a using the arithmetic and geometrical means.
It's probably simple, but I just can't figure it out.
I think it should be assumed a is a positive number. The problem doesn't have any conditions, but it's obviously false if a
I think it should be assumed a is a positive number. The problem doesn't have any conditions, but it's obviously false if a is negative.
2 Antworten
- sahsjingLv 7vor 9 JahrenBeste Antwort
It is not true.
Counter example:
a = -10
2a^3 + 11 = -2000 + 11 < 9a = -90
- multiplythebearLv 4vor 9 Jahren
If you want to prove that this is always true, you can't. For example, plug in -3.
2(-3)^3 + 11 > 9(-3)
2(-27) + 11 > -27
-54 + 11 > -27
-43 > - 27
Which is false.
