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    Need some help with the following question:

    |x-\sqrt{2}|>|x+3\sqrt{2}|

    What I did was square both sides so

    (x-\sqrt{2})^2>(x+3\sqrt{2})^2

    When I expanded I got

     x^2-2\sqrt{2}x+2>x^2+6\sqrt{2}x+18

    Then I got:

    -8\sqrt{2}x>16
    Divided by -8 and rationalised to get  x<-\frac{-2\sqrt{2}}{2}

    But the answer is  x<-\sqrt{2} or  -\sqrt{2}>x
    Which means I've messed up somewhere I think. Thanks in advance
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    (Original post by Super199)
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    Check step after  -8\sqrt{2}x > 16 .
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    (Original post by lazy_fish)
    Check step after  -8\sqrt{2}x > 16 .

    Right I could have cancelled down to get x<-\sqrt{2}

    Not sure how to get the other solution
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    (Original post by Super199)
    Need some help with the following question:

    |x-\sqrt{2}|>|x+3\sqrt{2}|

    What I did was square both sides so

    (x-\sqrt{2})^2>(x+3\sqrt{2})^2

    When I expanded I got

     x^2-2\sqrt{2}x+2>x^2+6\sqrt{2}x+18

    Then I got:

    -8\sqrt{2}x>16
    Divided by -8 and rationalised to get  x<-\frac{-2\sqrt{2}}{2}

    But the answer is  x<-\sqrt{2} or  -\sqrt{2}>x
    Which means I've messed up somewhere I think. Thanks in advance
    Multiplying or dividing an inequality by a negative number reverses the inequality sign
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    (Original post by brianeverit)
    Multiplying or dividing an inequality by a negative number reverses the inequality sign
    Haha I realised that, I was being daft and never realised that either of those answers are acceptable because they are the same thing. Grr. Thanks! by the way I remember you have C3 notes on MEI can I have those by any chance? (I some how lost the pdf thing)
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    (Original post by Super199)
    Haha I realised that, I was being daft and never realised that either of those answers are acceptable because they are the same thing. Grr. Thanks! by the way I remember you have C3 notes on MEI can I have those by any chance? (I some how lost the pdf thing)
    Here you are. Hope you find them useful.
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  1. File Type: pdfNotes for C1-C4.pdf (918.2 KB, 41 views)
 
 
 
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