fplot(@(x) sqrt(2x^2)) ;
hold on
fplot(@(x) sqrt(2x^2)) ;
fplot(@(x) abs((3x^3)^(1/3))*sign((3x^3)));
axis equal
grid on
plots this graph of the two functions, on either side of the equation.
The square function is real only between sqrt(2) and sqrt(2), and in this range is always below the cubic function, so there are no real solutions to the equation.
The closest the two curves come is cuberoot(3)  sqrt(2), at the top of the circle and at its right side.
Edited on December 27, 2023, 7:46 am

Posted by Charlie
on 20231227 07:42:48 