set A={x:^11+7^5+√5·^3+8<2} Prove that the number sup is a root of the function ()=^11+7^5+√5·^3+8−2 without using any differentiation and intermediate value theorem.
I want to know how to solve this problem using Axiom of Completeness and existence of square roots. Like the aim is to prove f(supA)>=0 and f(supA)>=0 so that we can conclude that f(supA)=0… or we can just ruling out the possibilities f(supA)>0 and f(supA)<0 ?? can anyone tell me the steps? thx!