SMO Open · 2. Equations, systems and word problems
Read absolute values as distances, turn radicals into absolute values through hidden squares, solve systems by subtracting equations or by a monotone function, and build equations from word problems through invariants.
Solve absolute-value equations and inequalities with the distance picture and the triangle-equality condition.
Solve radical equations with a domain, a substitution and a final check, without gaining or losing roots.
Solve symmetric systems with x + y and xy, and use strictly increasing functions to compare unknowns.
Translate a word problem into an equation through an invariant and prove a minimum with a bound and a construction.