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Homework Help: Help with an proof

  1. Oct 6, 2005 #1
    i need help proving that



    (sqrt(7+sqrt(48)))+(sqrt(7-sqrt(48))) = 4

    the limitations are that you cannot manipulate the right side...only the left..

    so basically, i need help simplifying the left down to be 4

    thanks..
     
  2. jcsd
  3. Oct 6, 2005 #2

    Fermat

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    Square the lhs.

    Hint:
    (a+b)(a-b) = (a² - b²)
     
  4. Oct 6, 2005 #3

    Diane_

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    Try multiplying the left by (sqrt(7 + sqrt(48))-(sqrt(7-sqrt(48)) on itself. Since that's 1, you won't be changing the value, but you'll find a few things simplifying.
     
  5. Oct 7, 2005 #4
    yea, i did that already, but the problem is, then i have complex radical denomintaors....
     
  6. Oct 7, 2005 #5

    arildno

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    You should use Fermat's squaring technique.
     
  7. Oct 7, 2005 #6
    wait a sec, what is the lhc......to not change the value, wouldnt i have to multiply it over itself if i wanted to get teh a^2 -B^2?

    can you clarify what you mean?
     
  8. Oct 7, 2005 #7

    arildno

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    Simplify the expression:
    [tex](\sqrt{7+\sqrt{48}}+\sqrt{7-\sqrt{48}})^{2}[/tex]
     
  9. Oct 7, 2005 #8
    that would change the value...i would have to also square the 4 on the right side...which is against the rules of the problem
     
  10. Oct 7, 2005 #9

    arildno

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    No.

    Define "x" as follows:
    [tex]x=\sqrt{7+\sqrt{48}}+\sqrt{7-\sqrt{48}}[/tex]
    Hence, we have:
    [tex]x^{2}=(\sqrt{7+\sqrt{48}}+\sqrt{7-\sqrt{48}})^{2}[/tex]
    That is:
    [tex]x^{2}=7+\sqrt{48}+2\sqrt{(\sqrt{7+\sqrt{48}})(\sqrt{7-\sqrt{48}})}+7-\sqrt{48}[/tex]
    that simplified reads:
    [tex]x^{2}=14+2\sqrt{49-48}=14+2*1=16[/tex]
     
  11. Oct 7, 2005 #10
    ok, thanks dude.........i got as far as your third step before i realized that you posted again...i realized my error...

    thanks for the great help guys!!!!
     
  12. Oct 12, 2005 #11
    just do the whole squaring thing, and instead of having 4^2 put it all under a radical ... that way you get sqrt ( 16) = 4 .. which is true to some extent, because -4^2 = 16 as well ..

    ... i hate that little thing so much
     
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