Germany | Olympiad Mathematics | Fully solved

[@robertgapatas]

±2

[@brianwade4179]

What you did is very complicated. Look. a^4+a^2-20=0. It's a quartic so we are expecting four solutions. Via u=a^2, u^2+u-20=0. From Rational Root Theorem, candidates are +-1, +-2, +-4, +-5, +-10, +-20. Owing to those large exponents, we should look at the small candidates first. u=4 works, giving us (u-4) as a factor, giving us (u-4)(u+5)=0, giving us u=-5. For u=4, a^2=4 gives us a=+-2. For u=-5, a^2=-5 gives us a=+-sqrt(5)i. a = {+2,-2,+sqrt(5)i,-sqrt(5)i}.