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Can't get this

  • Thread starter wisredz
  • Start date
  • #1
111
0
can't get this!!!

Hi there,
I have a question that I cannot solve. Here it is.

[tex]\frac{1}{\sqrt(4-2\sqrt3)}=x+y\sqrt3 [/tex]

then what is x^2+y^2?

All I did was finding what left hand side stood for. It equals

[tex]\frac{\sqrt3 + 1}{2} [/tex]

Any help?
 

Answers and Replies

  • #2
Wiz
21
0
if i understand u right then tht implies x=y=1/2......so find wht u want...
 
  • #3
111
0
How does he implies that? I got there before but I supposed that x and y are not irrational
 
  • #4
3,763
8
do you know the numerical solution for this problem ?

marlon
 
  • #5
3,763
8
hello ? are you dead ?
 
  • #6
HallsofIvy
Science Advisor
Homework Helper
41,833
955
If x and y are rational, then x= y= 1/2 so x2+ y2= 1/2 is the only solution. If x and y are allowed to be rational, then there are an infinite number of solutions.
 
  • #7
3,763
8
how is the left hand side equal to [tex]\frac{\sqrt3 + 1}{2} [/tex] ?


marlon
 
  • #8
111
0
that's because of this.

suppose that a=x+y and b=xy then

[tex]\sqrt (a + 2\sqrt b) = \sqrt x+ \sqrt y [/tex]

Ivy, I don't get what you mean. How do you know if the numbers x and y are rational then the only solution is x=y=0.5? and how do you know there is an infinite number of solutions if they are irrational?
 
  • #9
Wiz
21
0
if x and y are rational then irrational terms on both sides of the eq must be equal adn also rational terms on both sides must be equal.hence y=x=0.5....get it?
 
  • #10
111
0
yeah I know it, I said I did it that way. But the problem is that nothing is told about it. Anyway thnaks, I think the question wasn't complete in this case
 

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