恒等变形专题课4笔记

1、初中数学专题课代数式恒等变形-4主讲教师:52145208Update on 2016 年 2 月 16 日目录1例题精讲21海边代数式恒等变形-41例题精讲1.化简a b + b c + c a + (a b)(b c)(c a).a + bb + cc + a(a + b)(b + c)(c + a)2海边代数式恒等变形-4化简2.2 1 12()x + x2 x x + 32111x + x x +÷.1 1 2xx2 + x2 2x x + 31 x x3海边代数式恒等变形-4化简3.x2x3x4x1(x1 + x2) + (x1 + x2)(x1 + x2 + x3) +

2、(x1 + x2 + x3)(x1 + x2 + x3 + x4) +xn· · · · · · + (x1 + x2 +··· + xn 1)(x1 + x2 +··· + xn).4海边代数式恒等变形-4a2 + (a c)2222已知 a + b = (a + b c) , 并且 b = 0, 化简 b2 + (b c)2 .4.5海边代数式恒等变形-4ax2mnax若 x = m2 n = 0, 化简 mx n m .5.6海边代数式恒等变形-4化简6. (y x)(

3、z x)+(z y )(x y )+(x z)(y z).(x 2y + z)(x + y 2z)(x + y 2z)(y + z 2x)(y + z 2x)(x 2y + z)7海边代数式恒等变形-4b cc aa bbc b cca c aab a b + + + 7.若 a+b+c = 0, 且= 0. 求证:= 0.+b2c2c2 a2a2b2abc8海边代数式恒等变形-4111 是正数, 负数, 还是零?8.已知有理数 a, b, c 满足 a + b + c = 0, abc = 8. 试a + b + c9海边代数式恒等变形-4111 1a + b + c9.已知有理数 a, b

4、, c 满足 +=, 求证: a = b, 或 b = c, 或 c = a.abc10海边代数式恒等变形-4111110.若 n 为自然数, 且. 求证:a + b + c = a + b + c1111a2n+1 + b2n+1 + c2n+1 = a2n+1 + b2n+1 + c2n+1 .11海边代数式恒等变形-4证明对于任意自然数 n, 分数 21n + 4 不可约.14n + 311.12海边代数式恒等变形-4已知 a + b + c = 0, 且 a, b, c 都不等于 0. 求证:12.()()()111111ab + c+ bc + a+ ca + b+ 3 = 0.13

5、海边代数式恒等变形-4证明:13. 1 1 1 n 1+··· +=.a(a + d )(a + d )(a + 2d )a + (n 2)d a + (n 1)d aa + (n 1)d 14海边代数式恒等变形-4若 n 为正整数, 求证:14.11111 × 3 + 3 × 5 +··· + (2n 1)(2n + 1) < 2 .15海边代数式恒等变形-4 xyz 若 x + y + z = 0, x + y = 0, y + z = 0, z + x = 0, a =, b =, c =. 求证:15.y + zx + zx + yabca + 1 + b + 1 + c + 1 = 1.16海边代数式恒等变形-4设 a, b, c 均为正数, 且 a + b + c = 1. 证明:16.111a + b + c 9.17海边代数式恒等变形-4求证:17. b c+c a+a b= 2 + 2 + 2 .(a b)(a c)(b c)(b a)(c a)(c b)a bb cc a18海边代数式恒等变形-4 x + 3 .x(x2 1)