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Math Help - good question

  1. #1
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    good question

    What is the value of
    \frac{x + y + z}{a + b +c}<br /> <br />
    x^2 + y^2+ z^2=15<br /> <br />
    a^2 + b^2+ c^2=25

    ax +by + cz = 20
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  2. #2
    MHF Contributor red_dog's Avatar
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    Add the first and the second equalities and substract 2 times the third:

    x^2+y^2+z^2+a^2+b^2+c^2-2ax-2by-2cz=0

    (x-a)^2+(y-b)^2+(z-c)^2=0\Rightarrow x=a, \ y=b, \ z=c

    Then \frac{x+y+z}{a+b+c}=\frac{a+b+c}{a+b+c}=1
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  3. #3
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    Magnificent solution, red-dog!

    *cheers* . *applause*

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