mahmit2012
if x+sqrt(x)=1 what is the value of x^2+2x.sqrt(x)
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anonymous
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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
\[x^2+2\sqrt{x}=1-\frac{3-\sqrt{5}}{2}=\frac{2-3+\sqrt{5}}{2}=\frac{-1+\sqrt{5}}{2}\]
nickymarden
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where did you get x^2-3x+1=0 from? Oo
anonymous
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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
nickymarden
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no, you're right, i just didn't pay attention :P
anonymous
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you really in brazil?!
nickymarden
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haha yeah lol
anonymous
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wow.
anonymous
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near the ocean?
nickymarden
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10 min :P
anonymous
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nice
nickymarden
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so if i sometimes say something wrong in my questions, it's becaus i have to translate them all :)
anonymous
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from portuguese?
nickymarden
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yup. all of them :)
anonymous
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i am impressed
nickymarden
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be
anonymous
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why not? i can barely speak one language, and portuguese is way different than english
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
anonymous
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i bet brazil in nicer than england
nickymarden
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no way, i'm doing everything to go back. where are you from?
anonymous
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philadelphia
anonymous
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going back when you graduate? or sooner?
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
anonymous
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good luck! hope you get there soon.
nickymarden
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thank you :)