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Math Help - Any short method of solving these two equation

  1. #1
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    Any short method of solving these two equation

    Plz solve this equation in a shortest way
    X+root Y=7
    root X+Y+11
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  2. #2
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    Quote Originally Posted by sandeeptiwari674 View Post
    Plz solve this equation in a shortest way
    X+root Y=7
    root X+Y+11
    First, this doesn't really belong in "Linear and Abstract Algebra".

    I would solve x+ \sqrt{y}= 7 for x: x= 7- \sqrt{y}.

    Then replace x by that in the second equation:
    \sqrt{7- \sqrt{y}}+ y= 11
    (You have "+11" but without an "=" there is no equation so I assume you mean "=".)

    Now isolate the square root, \sqrt{7- \sqrt{y}= 11- y, and square both sides: 7- \sqrt{y}= 121- 22y+ y^2.

    Again, isolate the square root, -\sqrt{y}= y^2- 22y+ 114 and square both sides.
    y= y^4- 22y^3+ 114y- 22y^3+ 484y^2+ 2508y+ 114y^2- 2508y+ 196
    y= y^4- 44y^3+ 598y^2+ 484y+ 196 or
    y^4- 44y^3+ 598y^2+ 483y+ 196= 0.

    That is a fourth degree polynomial equaton which might be difficult to solve. The only possible rational roots are the factors of 196 so I would recommend trying those first.
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  3. #3
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    Quote Originally Posted by sandeeptiwari674 View Post
    Plz solve this equation in a shortest way
    X+\sqrt Y=7
    \sqrt X+Y=11
    I couldn't help noticing that
    4+\sqrt 9=7
    \sqrt 4+9=11.
    Try following HallsofIvy's method, checking at each step whether those numbers fit the equations. That should lead to a solution.
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