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Math Help - Variables of multi-equations

  1. #1
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    Variables of multi-equations

    The question is:

    a^3+6abd+3c(ac+b^2+d^2)=1
    b^3+6abc+3d(a^2+bd+c^2)=0
    c^3+6bcd+3a(ac+b^2+d^2)=0
    d^3+6acd+3b(a^2+bd+c^2)=0

    How to find the value of a,b,c,d?
    Thanks
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  2. #2
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    Hello, haedious!

    \begin{array}{ccc}a^3+6abd+3c(ac+b^2+d^2) &=& 1 \\<br />
b^3+6abc+3d(a^2+bd+c^2) &=& 0 \\<br />
c^3+6bcd+3a(ac+b^2+d^2) &=& 0 \\<br />
d^3+6acd+3b(a^2+bd+c^2) &=& 0 \end{array}

    By inspection: . \begin{Bmatrix}a &=& 1 \\ b &=& 0 \\ c&=&0 \\ d&=&0 \end {Bmatrix}

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  3. #3
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    Thank you quickly reply, seem I mess up something...
    But are there only the answer {1,0,0,0} to the question?
    What if I knew the value of a is equal to 0?
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  4. #4
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    Question

    Dear Soroban,

    Is there other ways of solving this question instead of by inspection.
    I notice there is some form of symmetry in the given equations which is some kind of cyclic order.
    Thanks
    Kingman
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