solve

2. ## Re: solve equation

Originally Posted by swarna
solve
Spoiler:
Okay, I solved it. Now what?

What have you been able to do with it? We can help you better if we know what you have tried.

-Dan

3. ## Re: solve equation

Hint: The solution involves a line and a circle. That is, there is no solution if the values of x and y lie on a particular line nor if they lie on a particular circle.

4. ## Re: solve equation

swarna You have two equations or system of them?

5. ## Re: solve equation

Find x,y from these equations

6. ## Re: solve equation

I tried in this way.
multiply the equation (1) by y and equation (2) by x. Now suppose these two equation become (3) and (4). now (3)+(4) & (3)-(4) i get another two equations and tried to solve them.

7. ## Re: solve equation

Originally Posted by swarna
I tried in this way.
multiply the equation (1) by y and equation (2) by x. Now suppose these two equation become (3) and (4). now (3)+(4) & (3)-(4) i get another two equations and tried to solve them.
Hint:
Spoiler:
Calculate $12 + 4 i$ where $i^2 = -1$

8. ## Re: solve equation

Thank you all.

9. ## Re: solve equation

Originally Posted by swarna
Thank you all.
$12+4i=5x + \frac{5x}{x^2+y^2}+5 i y -\frac{5 i y}{x^2+y^2}=5z+\frac{5}{z}$

where

$z=x+i y$

This leads to a quadratic in z with two solutions $z=2+i$ and $z=\frac{2}{5}-\frac{1}{5}i$

So x = 2 y = 1 and x = 2/5 and y = -1/5 are the two solutions of the system