Hi, could you help me with this solution:
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 not solution for me and I don't understand why the Sage gave me it. 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:
[ x == 3a + sqrt(9a^2 + 10) ]
Could you help me explain the difference in results. Thank you in advance.