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笔者在讲授“点到直线的距离公式”这一内容时,曾参考学习过熊昌进老师的文章《用柯西不等式推导点到直线的距离公式》,读后很是感慨!笔者发现,既然可以用柯西不等式推导点到直线的距离公式,那么也能用点到直线的距离公式来证明二维形态的柯西不等式,下面给出具体阐述.二维柯西不等式:若a1,a2,b1,b2∈R,则(a21+a22)(b21+b22)(a1b1+a2b2)2,当且仅当a1b2=a2b1时,等号成立.
The author taught “point to the line distance formula” of this content, had referred to the study of Xiong Changjin teacher’s article “Cauchy inequality derivation point-to-line distance formula”, after reading it is feeling! I found that since You can use the Cauchy inequality to derive the point-to-line distance formula, then you can also use point-to-line distance formula to prove the two-dimensional Cauchy inequality, given below. b1, b2∈R, then (a21 + a22) (b21 + b22) (a1b1 + a2b2) 2, and if and only if a1b2 = a2b1, the equal sign holds.