Task 691
Task 691: development task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. A square is inscribed in the ellipse \ \frac{x^2}{3} + \frac{y^2}{6} = 1,\ so that its sides are parallel to the coordinate axes. Find the area of the square. asy unitsize(1 cm); draw(xscale(sqrt(3))…
The task
A square is inscribed in the ellipse \[\frac{x^2}{3} + \frac{y^2}{6} = 1,\]so that its sides are parallel to the coordinate axes. Find the area of the square. [asy] unitsize(1 cm); draw(xscale(sqrt(3))*yscale(sqrt(6))*Circle((0,0),1)); draw((sqrt(2),sqrt(2))--(-sqrt(2),sqrt(2))--(-sqrt(2),-sqrt(2))--(sqrt(2),-sqrt(2))--cycle); draw((-2,0)--(2,0)); draw((0,-3)--(0,3)); [/asy]