IMO 1988 LL INA46

Origin: INA

Problem

(a) Calculate x = (11+6 \sqrt 2)\sqrt 11−6 \sqrt 2−(11−6 \sqrt 2)\sqrt 11+6 \sqrt (\sqrt\sqrt 5+2+\sqrt\sqrt 5−2)−(\sqrt\sqrt 5+1) . (b) For each positive number x, let k = (x+1/x)6−(x6+1/x6)−2 (x+1/x)3+(x3+1/x3) . Calculate the minimum value of k.