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Quick maths question c3 Factorising HELP please Watch

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    Say you have 2+x^1/2 = x (2 plus square root of x equals x)
    if I square the whole equation in attempt to get rid of the square root I get 4+x=x^2 and then rearranging this give x^2 - x -4=0 However this gives me the wrong solution.
    Even substituting x^1/2 as u gives 2+u=u^2 which again gives me the wrong solutions... what is the reason for this?? Because I'm so confused - the way to do it is moving the 2 over to the other side first to get x^1/2 = x-2 and then squaring to get x=(x-2)^2 and solving this gives me the correct answer but I don't understand how Im meant to know which order to go in - isnt this question just BIDMAS backwards?? and the squareroot is basically an indice of 1/2??

    Any help would mean the most

    This is also like substituting x^1/2 as u.
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    (Original post by MrToodles4)
    Say you have 2+x^1/2 = x (2 plus square root of x equals x)
    if I square the whole equation in attempt to get rid of the square root I get 4+x=x^2 and then rearranging this give x^2 - x -4=0 However this gives me the wrong solution.
    Even substituting x^1/2 as u gives 2+u=u^2 which again gives me the wrong solutions... what is the reason for this?? Because I'm so confused - the way to do it is moving the 2 over to the other side first to get x^1/2 = x-2 and then squaring to get x=(x-2)^2 and solving this gives me the correct answer but I don't understand how Im meant to know which order to go in - isnt this question just BIDMAS backwards?? and the squareroot is basically an indice of 1/2??

    Any help would mean the most

    This is also like substituting x^1/2 as u.
    You're squaring the LHS wrong in the first attempt.

    Substituting u in is probably the best way to do it. Solve 2+u=u^2 for u (Like you would solve a normal quadratic) and then that'll work.
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    (Original post by MrToodles4)
    Say you have 2+x^1/2 = x (2 plus square root of x equals x)
    if I square the whole equation in attempt to get rid of the square root I get 4+x=x^2
    No you dont. You get (2+x^{1/2})^2=x^2 - expand the LHS.

    Replace x^{1/2} with x-2 in the expanded form, simplifying it gives you the 'correct' form
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    (Original post by MrToodles4)
    Say you have 2+x^1/2 = x (2 plus square root of x equals x)
    if I square the whole equation in attempt to get rid of the square root I get 4+x=x^2 and then rearranging this give x^2 - x -4=0 However this gives me the wrong solution.
    Even substituting x^1/2 as u gives 2+u=u^2 which again gives me the wrong solutions... what is the reason for this?? Because I'm so confused - the way to do it is moving the 2 over to the other side first to get x^1/2 = x-2 and then squaring to get x=(x-2)^2 and solving this gives me the correct answer but I don't understand how Im meant to know which order to go in - isnt this question just BIDMAS backwards?? and the squareroot is basically an indice of 1/2??

    Any help would mean the most

    This is also like substituting x^1/2 as u.
    2+x^1/2 doesn't give 4+x - remember (2+x^1/2)(2+x^1/2) its kinda like a quadratic u should have 3 terms
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    (Original post by JammieDodger27)
    You're squaring the LHS wrong in the first attempt.

    Substituting u in is probably the best way to do it. Solve 2+u=u^2 for u (Like you would solve a normal quadratic) and then that'll work.
    Thank youuu
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    (Original post by RDKGames)
    No you dont. You get (2+x^{1/2})^2=x^2 - expand the LHS.

    Replace x^{1/2} with x-2 in the expanded form, simplifying it gives you the 'correct' form
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    (Original post by MrToodles4)
    Why doesn't submitting for 'u' work??
    It does.

    Solve it for u, then square the expression to get x since u is just root x.
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    move 2 to the other side and use your method and you get x = (x-2)^2 (I think you know what (x-2)^2 equals to), move all the terms on one side , solve the resulting quadratic equation
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    (Original post by RDKGames)
    It does.

    Solve it for u, then square the expression to get x since u is just root x.
    Thanks I realised - so it is an incorrect method to move the 2 over to the other side and then square?? (x-2)^2 because I get a different different answer doing it that way.
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    (Original post by MrToodles4)
    Thanks I realised - so it is an incorrect method to move the 2 over to the other side and then square?? (x-2)^2 because I get a different different answer doing it that way.
    It's still correct. Dunno where you're going wrong.
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    (a+b)(a+b) = a^2 + 2ab + b^2

    Does this help?
 
 
 
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