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Math Help - Simultaenous Eq. with two unknowns

  1. #1
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    Simultaenous Eq. with two unknowns

    (root)x+y=11, x+(root)y=7

    Can anyone help me to find the values of X and Y? Thanks.
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  2. #2
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    Possible Solution

    Quote Originally Posted by cheque View Post
    (root)x+y=11, x+(root)y=7

    Can anyone help me to find the values of X and Y? Thanks.
    Well, I just guessed and checked and found that x = 4 and y = 9.

    Equation 1: root(4) + 9 = 2 + 9 = 11 This checks out
    Equation 2: 4 + root(9) = 4 + 3 = 7 This also checks out

    I'll try to find the actual method for arriving at this conclusion.
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  3. #3
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    Quote Originally Posted by ajj86 View Post
    Well, I just guessed and checked and found that x = 4 and y = 9.

    Equation 1: root(4) + 9 = 2 + 9 = 11 This checks out
    Equation 2: 4 + root(9) = 4 + 3 = 7 This also checks out

    I'll try to find the actual method for arriving at this conclusion.
    Yeah, I got the answer through brute-forcing too. . Take your time and please update on your progress.
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  4. #4
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     \sqrt(x) = 11-y *
     x = 121 - 22y +y^2
     \sqrt(y) = 7-x
     y = 49 - 14x +x^2
     1444 - 1065 x + 272 x^2 - 28 x^3 + x^4 =0 *
    Try the factor of 1444 as roots. You should not search for a long time.
    I keep thinking there must be a more elegant solution but this is one.
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