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Math Help - Abstract Inequalities

  1. #1
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    Abstract Inequalities

    Can anyone help me confirm if I've solved this correctly?

    Many thanks.

    Q.
    If a^2+b^2=1 & c^2+d^2=1, show that ac + bd < 1.

    Attempt: a^2+b^2+c^2+d^2=2
    if a^2+c^2\geq2ac & b^2+d^2\geq2bd
    if 2ac+2bd\leq2
    if ac+bd\leq1...true
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  2. #2
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    Re: Abstract Inequalities

    Yes, that is a perfectly good proof.

    (Of course, a^2+ c^2\ge 2ac because (a- c)^2= a^2- 2ac+ c^2\ge 0.)
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  3. #3
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    Re: Abstract Inequalities

    Great. Thank you.
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