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  1. Paris la ville de l'amour
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    #1
    Let $x,\,y,\,z>0$ and $a,\,b,\,c$ be real numbers such that $x^2+a^2=y^2+b^2=z^2+c^2=1$.

    Prove that $(a+b+c)^2+(x+y+z)^2\ge 1$.

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    #2
    Quote Originally Posted by anemone View Post
    Let $x,\,y,\,z>0$ and $a,\,b,\,c$ be real numbers such that $x^2+a^2=y^2+b^2=z^2+c^2=1$.

    Prove that $(a+b+c)^2+(x+y+z)^2\ge 1$.

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    #3
    Last edited by Albert; January 4th, 2017 at 23:31.

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    Last edited by anemone; January 5th, 2017 at 09:09. Reason: Hide Solution In SP Tags

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    #5

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