Question: How to find symbolic extreme values under constrained equality ?

Unfortunately,  Optimization:-Maximize command in following example returns a not precise result (I use Maple 2020).

restart:
s1:= Optimization:-Maximize((x-2*y)/(5*x^2-2*x*y+2*y^2), {2*x^2 - y^2 + x*y=1})

Maple is running the following results:

I read help of  Maximize, It seems to be using only numerical methods .

Can't Maple find a symbolic solution for extreme values under such constrained inequality or equality conditions?

Ps:

For the correct  symbolic  solution, we can try to  use Mathematica 12.

Maximize[{(x - 2*y)/(5*x^2 - 2*x*y + 2*y^2), 
  2*x^2 - y^2 + x*y == 1}, {x, y}]

  We can compare numerical sizes of Optimal solution between maple and mathematica. 

Digits:=20;
sqrt(2.)/4.

Another Problem:

If I accept numerical solutions of maple ,how do I estimate errors without knowing the exact solution ?