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柯西不等式(a_1~2+a_2~2)(b_1~2+b_2~2)≥(a_1b_1+a_2b_2)~2当a_1/b_1=a_2/b_2时等号成立(此式在高中数学课本第三册65页上以习题形式出现)。它在中学物理解题中往往可以巧妙地解决一些较难的极值问题,兹举例明之。例1 一质量为m的物体放在水平面上,物体与平面间的摩擦系数为μ,如使物体移动,拉力F至少需要多大? 解:该物处于由静到动的临界状态时应满足:Fcosθ=μN=μ(mg-Fsinθ)
Cauchy inequality (a_1~2+a_2~2)(b_1~2+b_2~2)≥(a_1b_1+a_2b_2)~2 When a_1/b_1=a_2/b_2, the equal sign holds (this equation is third in the high school mathematics textbook. The book appeared on page 65 in the form of exercises.) It can often cleverly solve some of the more difficult extreme problems in the subject of high school comprehension. Example 1 An object with a mass of m is placed on a horizontal surface, and the friction coefficient between the object and the surface is μ. If the object is moved, what is the pull force F at least? Solution: When the object is in a critical state from static to dynamic, it should satisfy: Fcosθ=μN=μ(mg-Fsinθ)