Question

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

Answer 1

\[x+\sqrt{x}=1\]
\[\sqrt{x}=1-x\]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
\[x^2+2\sqrt{x}=1-\frac{3-\sqrt{5}}{2}=\frac{2-3+\sqrt{5}}{2}=\frac{-1+\sqrt{5}}{2}\]

Answer 2

where did you get x^2-3x+1=0 from? Oo

Answer 3

\[\sqrt{x}=1-x\] 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

Answer 4

no, you're right, i just didn't pay attention :P

Answer 5

you really in brazil?!

Answer 6

haha yeah lol

Answer 7

wow.

Answer 8

near the ocean?

Answer 9

10 min :P

Answer 10

nice

Answer 11

so if i sometimes say something wrong in my questions, it's becaus i have to translate them all :)

Answer 12

from portuguese?

Answer 13

yup. all of them :)

Answer 14

i am impressed

Answer 15

be

Answer 16

why not? i can barely speak one language, and portuguese is way different than english

Answer 17

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

Answer 18

i bet brazil in nicer than england

Answer 19

no way, i'm doing everything to go back. where are you from?

Answer 20

philadelphia

Answer 21

going back when you graduate? or sooner?

Answer 22

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

Answer 23

good luck! hope you get there soon.

Answer 24

thank you :)