HMMT November 2024 T8

Compute the unique real number $x<3$ such that

$\sqrt{(3-x)(4-x)}+\sqrt{(4-x)(6-x)}+\sqrt{(6-x)(3-x)}=x$

Dataset text NuminaMath olympiads. 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.