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

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In summary, the conversation revolves around finding the solution for the equation \frac{1}{\sqrt(4-2\sqrt3)}=x+y\sqrt3 and determining the value of x^2+y^2. The participants discuss the possibility of x and y being rational or irrational, and how that affects the number of solutions. The final conclusion is that if x and y are rational, then the only solution is x=y=1/2, while there are an infinite number of solutions if they are irrational. The original problem is deemed incomplete, as it does not provide enough information to find a specific solution.
  • #1
wisredz
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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?
 
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  • #2
if i understand u right then tht implies x=y=1/2...so find wht u want...
 
  • #3
How does he implies that? I got there before but I supposed that x and y are not irrational
 
  • #4
do you know the numerical solution for this problem ?

marlon
 
  • #5
hello ? are you dead ?
 
  • #6
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
how is the left hand side equal to [tex]\frac{\sqrt3 + 1}{2} [/tex] ?


marlon
 
  • #8
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
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
 

1. What is the purpose of finding x^2+y^2 in math problems?

Finding x^2+y^2 helps us to solve for unknown variables in equations, as well as to determine the distance between two points on a coordinate plane.

2. How do I solve for x^2+y^2 in a math problem?

To solve for x^2+y^2, you can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (longest side) is equal to the sum of the squares of the lengths of the other two sides. In other words, a^2 + b^2 = c^2.

3. Can I solve for x^2+y^2 if I don't know the value of either x or y?

Yes, you can still solve for x^2+y^2 if you have information about the relationship between x and y. For example, if you know that x and y are equal, you can substitute one variable for the other and solve for the resulting equation.

4. Is finding x^2+y^2 only applicable to geometry problems?

No, finding x^2+y^2 can also be used in algebraic equations. It can help to simplify expressions and solve for unknown variables.

5. Can I use a calculator to find x^2+y^2?

Yes, most scientific calculators have a button for squaring numbers. Simply enter the values of x and y, square them, and then add them together to find x^2+y^2.

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