Maple; Find real solutions

[Dollydaggerxo]

$$y = k^{2}-4kx+3 - \sqrt{k^2+x-1/2}=0$$

I need to find the range of k so that this equation has some real solutions, using Maple.

I have started off by typing 'soln1:=solve(y,x);' which gives me two solutions both involving k. I just need to know how to get maple to return the range of k so that soln1 is real.

I can do it by hand, because I would just find out where the roots were undefined, right ? and exclude that from the range. But no idea how to do this in maple!

Can anybody help?? Thanks

 

[mighty2000]

Hello there,

Thank you for sharing your question on the forum. I am a Maple expert and I would be happy to assist you with finding the range of k for which the given equation has some real solutions.

To find the range of k, we first need to solve the equation for k. We can do this by using the solve function in Maple, just like you have done for finding the solutions for x.

To solve for k, we can use the following command:

soln2 := solve(y,k);

This will give us two solutions involving x. Now, to find the range of k for which soln2 is real, we can use the isreal function in Maple. This function checks if the given expression is real or not.

We can use the following command to check if soln2 is real or not:

isreal(soln2);

If the output is "true", then it means that soln2 is real. If the output is "false", then it means that soln2 is not real. Therefore, to find the range of k for which soln2 is real, we can use the following command:

solve(isreal(soln2), k);

This will give us the range of k for which soln2 is real. You can also use the "assuming" command in Maple to specify the domain for k. For example, if you want to find the range of k for which soln2 is real and positive, you can use the following command:

solve(isreal(soln2), k, assuming k>0);

I hope this helps. Please let me know if you have any further questions. Good luck with your research!