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Scary Girl
Lv 6
Scary Girl asked in Science & MathematicsMathematics · 10 years ago

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.

Update:

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

Update 2:

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 Answers

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  • sahsjing
    Lv 7
    10 years ago
    Favorite Answer

    It is not true.

    Counter example:

    a = -10

    2a^3 + 11 = -2000 + 11 < 9a = -90

  • multiplythebear
    Lv 4
    10 years ago

    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.

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