Question

若x∈R,f(x)=x^2-x+1,g(x)=1/(x^2+x+1),试比较f(x)与g(x)的大小

Answer 1

x²-x+1=(x-1/2)²+3/4>0,f(x)>0.同理g(x)>0.

f(x)/g(x)=(x²-x+1)(x²+x+1)=(x²+1)²-x²=x^4+x²+1≥1

所以f(x)≥g(x).