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mahmit2012

if x+sqrt(x)=1 what is the value of x^2+2x.sqrt(x)

  • one year ago
  • one year ago

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  1. satellite73
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    \[x+\sqrt{x}=1\] \[\sqrt{x}=1-x\]x^2-3x+1=0 \[x=1-2x+x^2\] \[x^2-3x+1=0\] \[x=\frac{3-\sqrt{5}}{2}\] and \[1=(x+\sqrt{x})^2=x^2+2x\sqrt{x}+x\]so \[x^2+2\sqrt{x}=1-\frac{3-\sqrt{5}}{2}=\frac{2-3+\sqrt{5}}{2}=\frac{-1+\sqrt{5}}{2}\]

    • one year ago
  2. nickymarden
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    where did you get x^2-3x+1=0 from? Oo

    • one year ago
  3. satellite73
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    \[\sqrt{x}=1-x\] square both sides get \[x=(1-x)^2=1-2x+x^2\] set equal to zero to solve the quadratic get \[x^2-3x+1=0\] unless i goofed up

    • one year ago
  4. nickymarden
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    no, you're right, i just didn't pay attention :P

    • one year ago
  5. satellite73
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    you really in brazil?!

    • one year ago
  6. nickymarden
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    haha yeah lol

    • one year ago
  7. satellite73
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    wow.

    • one year ago
  8. satellite73
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    near the ocean?

    • one year ago
  9. nickymarden
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    10 min :P

    • one year ago
  10. satellite73
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    nice

    • one year ago
  11. nickymarden
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    so if i sometimes say something wrong in my questions, it's becaus i have to translate them all :)

    • one year ago
  12. satellite73
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    from portuguese?

    • one year ago
  13. nickymarden
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    yup. all of them :)

    • one year ago
  14. satellite73
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    i am impressed

    • one year ago
  15. nickymarden
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    be

    • one year ago
  16. satellite73
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    why not? i can barely speak one language, and portuguese is way different than english

    • one year ago
  17. nickymarden
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    yeah but i lived in england for a few years when i was little, so i still remember a few things. The hard part is to know scientific words, but MIT open course helps me with that lol

    • one year ago
  18. satellite73
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    i bet brazil in nicer than england

    • one year ago
  19. nickymarden
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    no way, i'm doing everything to go back. where are you from?

    • one year ago
  20. satellite73
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    philadelphia

    • one year ago
  21. satellite73
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    going back when you graduate? or sooner?

    • one year ago
  22. nickymarden
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    sooner, my dad works in reasearch and he knows a lot of people at some universities in england so i might try to get a transfer or something when he goes there to do his Post-doc

    • one year ago
  23. satellite73
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    good luck! hope you get there soon.

    • one year ago
  24. nickymarden
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    thank you :)

    • one year ago
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