若a＞0则a+(1/a)=[√a-(1/√a]^2+2≥2成立令x=a+(1/a)则a^2+1/a^2=x^2-2f(x)=x-√(x^2-2) =(x-√(x^2-2))(x+√(x^2-2))/(x+√(x^2-2)) =2/(x+√(x^2-2))其分母为增函数，当x=2时取最小值2+√2∴f(x)为减函数，当x=2时取最大值2-√2
