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If 2a+b+3c=1 and a gt 0, b gt 0, c gt 0...

If `2a+b+3c=1` and `a gt 0, b gt 0, c gt 0` , then the greatest value of `a^(4)b^(2)c^(2)"_____"`.

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The correct Answer is:
`a^(4)b^(2)c^(2) = (1)/(9.4^(8))`
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