1极化恒等式人教A版必修4第二章“平面向量应用举例”的例题1中,证明了平面几何中一个常见的结论,即“平行四边形两条对角线的平方和等于两条邻边平方和的两倍”.证明:(a+b)~2=|a|~2+|b|~2+2a·b,①(a-b)~2=|a|~2+|b|~2-2a·b,由①+②得(a+b)~2+(a-b)~2=2|a|~2+2|b|~2,即证.实则,把两个式子相减即可得到另一个常用结论,及“极化恒等式”. 1 Polarization Identity Hypothesis A Compulsory 4 Chapter 2, “Example of Plane Vector Applications”, shows a common conclusion in plane geometry that the sum of the squares of the two diagonals of a parallelogram equals Prove that: (a + b) ~ 2 = | a | ~ 2 + | b | ~ 2 + 2a · b, ① (ab) ~ 2 = | a | ~ 2 + | b | ~ 2-2a · b, from ① + ② was (a + b) ~ 2 + (ab) ~ 2 = 2 | a | ~ 2 + 2 | b | ~ 2, Subtracting two formulas yields another common conclusion, and “polarization identity”.