Wrong solution?
Hi, could you help me with this solution of two equations on the interval:
x,a=var('x,a')
f1=10/x
f2=x-5*a
assume(a>0,x>0)
print(solve([f1==f2],x))
Solution given by Sage is:
[ x == 5/2a - 1/2sqrt(25*a^2 + 40),
x == 5/2a + 1/2sqrt(25*a^2 + 40) ]
The first solution is obviously not solution for me as it is always strictly negative and I don't understand why the Sage gave me it. Assumptions are clear: x has to be >0 When I change second equation slightly:
x,a=var('x,a')
f1=10/x
f2=x-6*a
assume(a>0,x>0)
print(solve([f1==f2],x))
Solution given by Sage is correct now (only the x>0 are reported):
[ x == 3a + sqrt(9a^2 + 10) ]
Could you help me explain the difference in results. I am not sure if problem is on python side or with some rules how Sage computes the results. Thank you in advance.