A Nice Rational Equation from Crux Mathematicorum

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[@dwm1943]

That's great. I didn't have a clue about this one, and you made it easy - method 2.

[@scottleung9587]

Nice!

[@Qermaq]

This was fun to solve. My aha moment was seeing that I could add 12x and make a perfect fourth power. Then it turned nicely into two similar quadratics which were not fun to solve.

[@FaerieDragonZook]

k=0, since 12y^2+24y+12 = (2 sqrt(3) (y+1))^2

[@ناصريناصر-س4ب]

After noting that 1 is not a solution to the equation, we can put x=y+1/y-1 and get the quadratic equation 3y⁴-6y²-1=0. By solving this equation with the unknown y, we deduce the solutions to the equation with the unknown x.