(In reply to
based on Wolfram Alpha by Charlie)
Indeed (x,y) = (√2/2,√2/2) solves the equation and x+y = √2
But (x,y) = (0.965926, 0.965926) also solves the equation,
and x+y =
1.931852 which is √(2 + √3)
In Wolfram Alpha if you put in:
(4x^33x)^2+(4y^33y)^2=1 intersects y=x
The graph shows a circle and 2 "ellipses" (or at least similar to ellipses) one with the long axis along the y=x line and the other along the y=x line. The line y=x intersects both the circle which gives one result and both ellipses which gives the larger result above, as well as a smaller result of (0.258819, 0.258819) which is (√(2  √3))/2

Posted by Larry
on 20231112 18:32:50 