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TeemoTheTerific Group Title

help me on a question please... x= 1/2 +1/2sqrt5 show that...

  • one year ago
  • one year ago

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  1. TeemoTheTerific Group Title
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    \[x=\frac{ 1 }{ 2 } + \frac{ 1 }{ 2 }\sqrt{5}\]

    • one year ago
  2. TeemoTheTerific Group Title
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    \[\frac{ x^{2}+x ^{-2} }{ x-x ^{-1} }=3\]

    • one year ago
  3. Azteck Group Title
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    \[x=\frac{1}{2}+\frac{\sqrt{5}}{2}\] \[x=\dfrac{1+\sqrt{5}}{2}\]

    • one year ago
  4. enka Group Title
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    \[x=\frac{1+\sqrt{5}}{2}\\ \frac{1}{x}=\frac{2}{1+\sqrt{5}}\times\frac{\sqrt{5}-1}{\sqrt{5}-1}=\frac{2\sqrt{5}-1}{4}=\frac{\sqrt{5}-1}{2}\] then \[x-\frac{1}{x}=1\qquad(1)\] square both side to get: \[x^2+\frac{1}{x^2}-2=1\\ x^2+\frac{1}{x^2}=3\qquad(3)\] now divide (3) by (1) to get the result

    • one year ago
  5. Azteck Group Title
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    \[x^2+x^{-2}=3x-3x^{-1}\] Multiply both sides by x^2. \[x^4+1=3x^3-3x\] \[x^4-3x^3+3x+1=0\]

    • one year ago
  6. TeemoTheTerific Group Title
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    i dont get it... both of you :P

    • one year ago
  7. TeemoTheTerific Group Title
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    yes ok

    • one year ago
  8. enka Group Title
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    first, we find the value of \[x-\frac{1}{x}\]

    • one year ago
  9. Azteck Group Title
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    You just sub in \[\frac{1+\sqrt{5}}{2}\] into the original equation....

    • one year ago
  10. Azteck Group Title
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    And you prove that the LHS=RHS.

    • one year ago
  11. TeemoTheTerific Group Title
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    but no matter how manytimes i try i can never get it to equal 3

    • one year ago
  12. Azteck Group Title
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    Use a calculator if you can't do it....Use a calculator to solve the denominator first. You get one as the denominator...

    • one year ago
  13. Azteck Group Title
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    Jeez, you have a tool that can help you but you don't want to use it.

    • one year ago
  14. Azteck Group Title
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    You get 3 as the denominator when you plug the values into the numerator...

    • one year ago
  15. Azteck Group Title
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    numerator*

    • one year ago
  16. TeemoTheTerific Group Title
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    we need to show our working our using our skill of indices laws... But i dont have much

    • one year ago
  17. Azteck Group Title
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    There's no indice work when you learn that \[x^{-1}=\frac{1}{x^1}\] \[x^{-2}=\frac{1}{x^2}\]

    • one year ago
  18. Azteck Group Title
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    Dude, now once you see the letter x, put that big fat fraction into your calculator and get your values...

    • one year ago
  19. Azteck Group Title
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    I can solve that by hand but that will take me ages, to write it on the computer, so no thank you...

    • one year ago
  20. enka Group Title
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    i hope it is can help you

    • one year ago
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  21. enka Group Title
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    or this

    • one year ago
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  22. TeemoTheTerific Group Title
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    thank you enka

    • one year ago
  23. enka Group Title
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    you're welcome :)

    • one year ago
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