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  1. Paris la ville de l'amour
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    #1
    Let $a,\,b,\,c,\,d\in \mathbb{R}$ with condition that $a+b\sqrt{2}+c\sqrt{3}+2d\ge \sqrt{10(a^2+b^2+c^2+d^2)}$.

    Prove that $a^2+d^2=b^2+c^2$.

  2. Paris la ville de l'amour
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    #2 Thread Author
    Quote Originally Posted by anemone View Post
    Let $a,\,b,\,c,\,d\in \mathbb{R}$ with condition that $a+b\sqrt{2}+c\sqrt{3}+2d\ge \sqrt{10(a^2+b^2+c^2+d^2)}$.

    Prove that $a^2+d^2=b^2+c^2$.
    Hint:


  3. MHB Master
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    #3

  4. Paris la ville de l'amour
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    Thanks kaliprasad for participating and the nice solution, I solved it a bit different than yours:


  5. MHB Master
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    #5
    Quote Originally Posted by anemone View Post
    Thanks kaliprasad for participating and the nice solution, I solved it a bit different than yours:

    Last edited by kaliprasad; January 19th, 2016 at 22:16.

  6. Paris la ville de l'amour
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    Argh...sorry kaliprasad, last night I wasn't feeling okay and therefore the solution that I posted (with typo) in a hurry didn't quite hold water.

    I therefore want to give the reasoning that I've "in my mind" that would definitely work, to amend the incomplete solution I posted yesterday:


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