I'm little bit stuck with this system of equations : x^y=y^x and x^3=y^2 An obvious solution is (x,y)=(1,1) but what about the solution (9/4,27/8) ? I know the relation a^r=e^(r log a) but it doesn't help me.Thanks
Lorelei Patterson
Answered question
2022-07-21
How to solve this kind of equation I'm little bit stuck with this system of equations : and An obvious solution is but what about the solution ? I know the relation but it doesn't help me. Thanks
Answer & Explanation
thenurssoullu
Beginner2022-07-22Added 13 answers
Besides the easy solution you can do the following: Take on both sides of both equations to have:
Divide side by side (and here you should note that is a solution and hence, we cannot divide by or , otherwise we have the following), to come up with:
Divide side by side (and here you should note that is a solution and hence, we cannot divide by or , otherwise we have the following), to come up with:
Since the equation can also be written as: provided , we have that:
which leads to the desired result. Hope this helps. Cheers!
Almintas2l
Beginner2022-07-23Added 6 answers
Note that the second equation gives for arbitrary and divide the first equation by this to get
Now choose so that and either or This gives or which gives (anomalous solution ) or