证明:1.(1+x1)(1+x2)...(1+xn)≥(2√x1)*(2√x2)...(2√xn)=2^n√(x1 *x2*x3...*xn)=2^n2.因为a^4+a^2+1=(a^2+a+1)(a^2-a+1)所以3(1+a^2 + a^4)≥(1+a+a^2）^2<==>3(a^2-a+1)≥(a^2+a+1)<==>2a^2-4a+2≥0<==>2(a- 展开
证明:1.(1+x1)(1+x2)...(1+xn)≥(2√x1)*(2√x2)...(2√xn)=2^n√(x1 *x2*x3...*xn)=2^n2.因为a^4+a^2+1=(a^2+a+1)(a^2-a+1)所以3(1+a^2 + a^4)≥(1+a+a^2）^2<==>3(a^2-a+1)≥(a^2+a+1)<==>2a^2-4a+2≥0<==>2(a-1)^2≥0上式恒成立.所以3(1+a^2 + a^4)≥(1+a+a^2）^2 收起
