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Math Help - I need help!!!

  1. #1
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    Question I need help!!!

    Hi ppl I really need help in some exercise!!!

    it's about comparison.(what is smaller,bigger...)
    1)Nth root seventeen ___ Nth root 6 + Nth root 3
    2)Nth root seven + Nth root five ____ Nth root 2 + Nth root twelve

    3) x+4= Nth root (inside of it: 3x^2+5x-4)

    4) (x^2+3x)^2 -14(x^2 +3x) +40 = 0
    5) (x+6/x)^2 -12(x+6/x)+35=0


    plz help me!!!!!!! i will be grateful to the one who show mw how i need solve atleast one of those...

    p.s
    i solve(with your help,thank you!!!) all the exercise except number 3.help plz:]
    Last edited by katia15; August 25th 2007 at 01:20 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by katia15 View Post
    4) (x^2+3x)^2 -14(x^2 +3x) +40 = 0
    Put y=x^2+3x, then:

    y^2-14y+40=0

    which has roots y=4 and y=10, so now solve:

    x^2+3x=4

    (roots are by inspection x=-4, x=1)

    and

    x^2+3x=10

    (roots are by inspection x=-5 and x=2)

    to find all the x's that satisfy the original equation.

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by katia15 View Post
    5) (x+6/x)^2 -12(x+6/x)+35=0
    Same trick as for (4), put y=x+6/x, to get y^2-12y+35=0, and take it from there.

    RonL
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  4. #4
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    Hello, katia15!

    It's about comparison: less than or greater than.

    1)\; \sqrt[n]{17}\;\; ^{>}_{<} \;\;\sqrt[n]{6}+ \sqrt[n]{3}
    I assume that the inequality holds for any positive interger n.


    Let's test it for n=2.

    We have: . \sqrt{17} \;\;^{>}_{<}\;\;\sqrt{6} + \sqrt{3}

    Square both sides: . \left(\sqrt{17}\right)^2\;\;^{>}_{<}\;\;\left(\sqr  t{6} + \sqrt{3}\right)^2

    And we have: . 17 \;\;^{>}_{<}\;\;6 + 2\sqrt{18} + 3\quad\Rightarrow\quad8\;\;^{>}_{<}\;\;2\sqrt{18}\  quad\Rightarrow\quad 4\;\;^{>}_{<}\;\;\sqrt{18}

    Square both sides: . (4)^2\;\;^{>}_{<}\;\;\left(\sqrt{18}\right)^2\quad  \Rightarrow\quad 16\;\;^{>}_{<}\;\;18

    Since 16 < 18, the original inequality is "less than".


    Therefore: . \sqrt[n]{17}\;\;{\color{red}<}\;\;\sqrt[n]{6} + \sqrt[n]{3}

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  5. #5
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    thanks:)

    hi i wanted to sat thank you for CaptainBlack and soroban.
    you helpes me a lot
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