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Math Help - Simplify and solve!!!

  1. #1
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    Simplify and solve!!!

    Solve for k in
    <br />
4k-1=\sqrt{\frac{(k-2)^2+(k)^2+(k)^2+(5k-2)^2}{4}-(4k-1)^2}
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  2. #2
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    1) Square both sides

    2) Expand both sides fully

    3) Group like terms

    4) Solve.
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  3. #3
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    4(4k-1)^2=k^2-4k+4+k^2+k^2+25k^2-10k+4-4(16k^2-8k+1)
    4(16k^2-8k+1)=k^2-4k+4+k^2+k^2+25k^2-10k+4-64k^2+32k-4
    64k^2-32k+4=k^2-4k+4+k^2+k^2+25k^2-10k+4-64k^2+32k-4

    this is my wrong attempt.
    Last edited by Punch; February 23rd 2010 at 03:44 AM.
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  4. #4
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    Quote Originally Posted by Punch View Post
    4(4k-1)^2=k^2-4k+4+k^2+k^2+25k^2-10k+4-4(16k^2-8k+1)
    4(4k^2-8k+1)=k^2-4k+4+k^2+k^2+25k^2-10k+4-64k^2+32k-4
    16k^2-32k+4=k^2-4k+4+k^2+k^2+25k^2-10k+4-64k^2+32k-4

    this is my wrong attempt.
    Wrong or just incomplete?
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  5. #5
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    grouping them, i will get -52k^2+50k=0 which simplifies to

    -26k^2+25k=0

    which is wrong...
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  6. #6
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    I get...

    Quote Originally Posted by Punch View Post
    16k^2-32k+4=k^2-4k+4+k^2+k^2+25k^2-10k+4-64k^2+32k-4
    16k^2-32k+4=-36k^2+4+18k

    20k^2-50k=0

    10k(2k-5)=0

     k = 0,\frac{5}{2}
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  7. #7
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    from 16k^2-32k+4=-36k^2+4+18k,

    16k^2+36k^2-32k-18k=0
    52k^2-50k=0

    shouldn't it be done like this?
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  8. #8
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    I'm getting 0.2955 and -0.55919

    The answer is ~0.4 (according to Microsoft Maths).
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  9. #9
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    Quote Originally Posted by pickslides View Post
    I get...



    16k^2-32k+4=-36k^2+4+18k

    20k^2-50k=0

    10k(2k-5)=0

     k = 0,\frac{5}{2}
    pickslides's answer is correct accordingly to the answer. However, I do understand his workings, let's wait for him to show us how to solve it properly.
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  10. #10
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    ok then it's all good.

    I am also wanting to know.
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  11. #11
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    Quote Originally Posted by Punch View Post
    4(4k-1)^2=k^2-4k+4+k^2+k^2+25k^2-10k+4-4(16k^2-8k+1)
    4(4k^2-8k+1)=k^2-4k+4+k^2+k^2+25k^2-10k+4-64k^2+32k-4
    This should be [/tex]4(16k^2- 8k+ 1)= [/tex]
    16k^2-32k+4=k^2-4k+4+k^2+k^2+25k^2-10k+4-64k^2+32k-4

    this is my wrong attempt.
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  12. #12
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    Thanks... It's getting more and more confusing... seriously need someone to show the full workings.
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  13. #13
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    4(16k^2-8k+1)=k^2-4k+4+k^2+k^2+25k^2-10k+4-16k^2-8k+1
    64k^2-32k+4=12k^2-22k+8
    52k^2-10k-4=0

    it's still wrong, curious about how pickslides got the answer...
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