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Math Help - Abstract Inequalities

  1. #1
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    Abstract Inequalities

    Having a bit of trouble with this one. Can anyone help?

    Many thanks.

    Q.
    Prove a^2+2ab+2b^2\geq0

    Attempt: My original solution was going to be...: if (a+b)(a+2b)\geq0

    However, this does not fit the format of (real no.)2 > 0

    The alternative method I've found goes as follows: a^2+2ab+2b^2\geq0
    if a^2+4ab+4b^2\geq0
    if (a+b)^2...true, since (a+b)2 > 0

    Is this 2nd approach correct? How did they go from a^2+2ab+2b^2\geq0 to a^2+4ab+4b^2\geq0?
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  2. #2
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    Re: Abstract Inequalities

    Quote Originally Posted by GrigOrig99 View Post
    Q. [/B]Prove a^2+2ab+2b^2\geq0
    (a+b)^2+b^2\ge 0~.
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  3. #3
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    Re: Abstract Inequalities

    Ok, thank you.
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