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Math Help - Needing help in this question

  1. #1
    Newbie findmehere.genius's Avatar
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    Red face Needing help in this question

    Q. The no. of distinct pairs of (a, b) real numbers that would satisfy x=x^3+y^4and y=2xy.
    A-5
    B-12
    C-3
    D-7

    dont laugh anyone on such elementary question....help!!
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  2. #2
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    earboth's Avatar
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    Quote Originally Posted by findmehere.genius View Post
    Q. The no. of distinct pairs of (a, b) real numbers that would satisfy x=x^3+y^4and y=2xy.
    A-5
    B-12
    C-3
    D-7

    dont laugh anyone on such elementary question....help!!
    I've found 5 pairs of real numbers (and 2 pairs of complex numbers).

    \left|\begin{array}{rcl}x&=&x^3+y^4 \\y&=&2 x y\end{array}\right. \implies \left|\begin{array}{rcl}x(1-x^2)-y^4&=&0 \\y(1-2x)&=&0\end{array}\right.

    All results containing y = 0 satisfy the second equation. From the first equation you'll get 3 different values of x if y = 0.

    From the second equation you find out that x = \frac12 must be a possible x-value. Plug in this value into the first equation and calculate the corresponding y-values.
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  3. #3
    Newbie findmehere.genius's Avatar
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    Thanks for the answer...now some paperwork needed to get them into head.
    Last edited by mr fantastic; October 28th 2009 at 03:42 AM. Reason: Moved question to new thread
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