Hello, yoman360!

Please check for typos.

The best I can do is reduce it to a cubic equation with no rational roots.

Solve for

We see that neither nor is a root of the equation.

Divide by

. . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . .

Square both sides: . . . . . . . . . . . .

. . . . . . . . .

And we have: . . . .

. . This cubic equation has no rational roots.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

I realize that the roots need not be rational.

For example, if , then could be a root . . . (It isn't.)

And if , then could be a root . . . (It isn't.)

At this point, I surrendered . . .