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Math Help - First Proofs class.

  1. #1
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    First Proofs class.

    So the semester just started and im already drowning. Im usually pretty good at math but I just dont get proofs.

    I need help with a few problems (ive already attempted them multiple times), ill just post one at a time.

    The first one:
    from 'Mathematical Thinking Problem Solving and Proofs 2nd ed.'
    1.29
    Let x,y,z be nonnegative real numbers such that y+z > or = to 2.
    Prove: (x+y+z)^2 is > or = 4x + 4yz

    My attempt
    I expanded the square and canceled out what I could.

    Than I attempted different things from moving the right side over to the left and seeing if I could simply, or grouping the left and seeing if they broke down into smaller elements..

    This is not graded homework just practice but the quizzes are very similar to the HW im told so I need to understand this.

    Thanks in advance!
    Last edited by mr fantastic; January 16th 2012 at 02:41 PM. Reason: Title.
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  2. #2
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    Re: First Proofs class - HELP!

    Quote Originally Posted by resjsu View Post
    Let x,y,z be nonnegative real numbers such that y+z > or = to 2.
    Prove: (x+y+z)^2 is > or = 4x + 4yz
    To do this you must know this:
    \left( {\forall a\;\& \;b} \right)\left[ {a^2  + b^2  \ge 2ab} \right].

    \begin{align*}(x+y+z)^2&=x^2+y^2+z^2+2xy+2xz+2yz\\  &\ge x^2+2x(y+z)+4yz  \end{align*}
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  3. #3
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    Re: First Proofs class - HELP!

    Hello,
    Thank you replying.

    Can you explain how you got the right side?

    Where did the x^2 and the 2x(y+z) come from?

    I understand that if y+z equals at least 2 then the term turns into the original 4x but how did you know to look at that. Thats the trouble im having I don't know where to look for clues. I would've never thought of that.
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  4. #4
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    Re: First Proofs class - HELP!

    Can someone please explain?
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  5. #5
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    Re: First Proofs class - HELP!

    Quote Originally Posted by resjsu View Post
    Can someone please explain?
    Can YOU expand (x+y+z)^2~?
    If not then you have no business even attempting this problem.
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  6. #6
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    Re: First Proofs class - HELP!

    Of course I can, I stated that in the first post, its the right side I am not following.
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