求证:不论x取何实数,多项式(x-1)*(x-3)*(x-4)*(x-6)的值不小于-9

问题描述:

求证:不论x取何实数,多项式(x-1)*(x-3)*(x-4)*(x-6)的值不小于-9

(x-1)*(x-3)*(x-4)*(x-6)=[(x-1)(x-6)][(x-3)(x-4)]=[(x^2-7x)+6][(x^2-7x)+12]=(x^2-7x)^2+18(x^2-7x)+72令t=x^2-7x则(x-1)*(x-3)*(x-4)*(x-6)=t^2+18t+72=(t+9)^2-9>=-9因此命题得证...