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Math Help - basic

  1. #1
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    basic

    let a,b,c real no's such that a+2b+c=4 then find max value of (ab + bc + ac)

    (ans=4)
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  2. #2
    Senior Member TheAbstractionist's Avatar
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    a+2b+c=4\,\implies\,b=\frac{4-(a+c)}2

    If you substitute this into ab+bc+ca and simplify, I think you should get

    ab+bc+ca\ =\ 4-\frac{(a-2)^2}2-\frac{(c-2)^2}2

    Hence ab+bc+ca\,\le\,4 for all a,b,c\in\mathbb R.
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  3. #3
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    favour

    sir can you please add the simplification part actually i could not manage to get to the simplified form
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  4. #4
    Senior Member TheAbstractionist's Avatar
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    ab+bc+ca\,=\,b(a+c)+ac

    =\,\frac{(4-(a+c))(a+c)}2+ac

    =\,\cdots

    Carry on from there.
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