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Math Help - Inequality Proof question

  1. #1
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    Inequality Proof question

    Hi my first post! Feel embarrassed I cant see the solution as I though I was getting quite good at these.... Any here is the question:

    If a2 + b2 = 1 = c2 + d2 ; a, b, c, d are elements of R

    Prove that ab + cd < 1

    Apologies I cant seem to use superscript; the number 2 in the question is meant to be to the power of 2 for each of the letters in the equation.
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  2. #2
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    Quote Originally Posted by Abromavich View Post
    Apologies I cant seem to use superscript; the number 2 in the question is meant to be to the power of 2 for each of the letters in the equation.
    Why not learn to post in symbols? You can use LaTeX tags
    [tex]x^{-2}+y^{10}[/tex] gives x^{-2}+y^{10}

    [tex]ab+cd<1[/tex] gives ab+cd<1

    Quote Originally Posted by Abromavich View Post
    If a^2 + b^2 = 1 = c^2 + d^2 ; a, b, c, d are elements of R
    Prove that ab + cd < 1
    Note that a^2+b^2\ge 2ab~\&~c^2+d^2\ge 2cd.
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  3. #3
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    Thanks will use latex from now on. How do you know that ab=cd
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  4. #4
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    Quote Originally Posted by Abromavich View Post
    Thanks will use latex from now on. How do you know that ab=cd
    More importantly, we know that 2ab\le a^2+b^2=1.
    Now add the two and divide by 2.
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  5. #5
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    lol so simple, thanks for the help. Ill prob be back very soon
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