Question

设X大于等于1,求证:X的三次方大于等于X的平方减X加1?

Answer 1

即证明X^3≥X^2-X+1 X^3-(X^2-X+1)=x^3-x^2+x-1=x^2(x-1)+(x-1)=(x^2+1)(x-1) 因为x≥1 所以x-1≥0 x^2+1>0 (x^2+1)(x-1)≥0 X^3-(X^2-X+1)≥0 X^3≥X^2-X+1 x^3是x的3次方,x^2是x的平方