Stuck on Math Problem: Finding x^2+y^2

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Homework Help Overview

The problem involves finding the values of x and y in the equation \(\frac{1}{\sqrt{4-2\sqrt{3}}}=x+y\sqrt{3}\) and subsequently determining \(x^2+y^2\). The context is rooted in algebra and rationality of numbers.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the implications of assuming x and y are rational, with some suggesting specific values for x and y based on this assumption. Others question the validity of these assumptions and explore the possibility of irrational solutions.

Discussion Status

The discussion is ongoing, with various interpretations being explored regarding the nature of x and y. Some participants have provided reasoning based on rationality, while others express uncertainty about the completeness of the problem statement.

Contextual Notes

There is a lack of clarity regarding whether x and y are restricted to rational numbers, which has led to differing conclusions among participants. The original problem does not specify this, contributing to the complexity of the discussion.

wisredz
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can't get this!

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

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

then what is x^2+y^2?

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

\frac{\sqrt3 + 1}{2}

Any help?
 
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if i understand u right then tht implies x=y=1/2...so find wht u want...
 
How does he implies that? I got there before but I supposed that x and y are not irrational
 
do you know the numerical solution for this problem ?

marlon
 
hello ? are you dead ?
 
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.
 
how is the left hand side equal to \frac{\sqrt3 + 1}{2} ?


marlon
 
that's because of this.

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

\sqrt (a + 2\sqrt b) = \sqrt x+ \sqrt y

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?
 
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
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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