Math Olympiad Question l Can you solve given System of Equations ?

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[@wes9627]

ab=-1/2; a^2+(1-a)^2-2=2a^2-2a-1=0 yields a=(2±2√3)/4=(1±√3)/2 and b=-1/(2a)=(1∓√3)/2
a^11+b^11=30.90625

[@RealQinnMalloryu4]

(0)+(1)=1 (b ➖ 1a+1). (1)+(1)=2 (b ➖ 1a+1). {a^11+a^11 ➖}+{b^11+b^11 ➖}={a^22+b^22}=ab^44 ab^22^22 ab^2^1^1^1 ab^2^1 (ab ➖ 2ab+1).