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TeemoTheTerific

  • 3 years ago

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

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  1. TeemoTheTerific
    • 3 years ago
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    \[x=\frac{ 1 }{ 2 } + \frac{ 1 }{ 2 }\sqrt{5}\]

  2. TeemoTheTerific
    • 3 years ago
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    \[\frac{ x^{2}+x ^{-2} }{ x-x ^{-1} }=3\]

  3. Azteck
    • 3 years ago
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    \[x=\frac{1}{2}+\frac{\sqrt{5}}{2}\] \[x=\dfrac{1+\sqrt{5}}{2}\]

  4. enka
    • 3 years ago
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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

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

  6. TeemoTheTerific
    • 3 years ago
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    i dont get it... both of you :P

  7. TeemoTheTerific
    • 3 years ago
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    yes ok

  8. enka
    • 3 years ago
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    first, we find the value of \[x-\frac{1}{x}\]

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

  10. Azteck
    • 3 years ago
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    And you prove that the LHS=RHS.

  11. TeemoTheTerific
    • 3 years ago
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    but no matter how manytimes i try i can never get it to equal 3

  12. Azteck
    • 3 years ago
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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...

  13. Azteck
    • 3 years ago
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    Jeez, you have a tool that can help you but you don't want to use it.

  14. Azteck
    • 3 years ago
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    You get 3 as the denominator when you plug the values into the numerator...

  15. Azteck
    • 3 years ago
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    numerator*

  16. TeemoTheTerific
    • 3 years ago
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    we need to show our working our using our skill of indices laws... But i dont have much

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

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

  19. Azteck
    • 3 years ago
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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...

  20. enka
    • 3 years ago
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    i hope it is can help you

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  21. enka
    • 3 years ago
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    or this

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  22. TeemoTheTerific
    • 3 years ago
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    thank you enka

  23. enka
    • 3 years ago
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    you're welcome :)

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