UA-UMO 1997 Problem 115

Find all real solutions to the equation:

$(2+\sqrt{3})^x+1=\left( 2\sqrt{2+\sqrt{3}} \right)^x$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.