SMO Open · 1. Algebraic expressions, radicals, exponents and logarithms
Spot the hidden square, the symmetric quantity, the mirror function or the conjugate partner, and the long computation becomes short.
Denest square roots and handle the domain of radicals correctly.
Compute symmetric expressions from $x\pm\frac1x$ or $a+b+c=0$ without solving for the variables.
Use the definition and graphs of exponentials and logarithms, including uniqueness of roots.
Find integer parts with conjugates and evaluate long sums by pairing.