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# 代数式与恒等变形专题

19993?10003?9993m2?m?22 解关于x方程 m?1? x1999?1000?999

1222992

??...?212?100?500022?200?500099?9900?5000

x?13x?1?求0 x?

241个位数字 x4

x2?3y2?5z2

12963x+3y+5z=0,2x+4y+7z=0求2 分解因式 a?a?a?a?1 222x?4y?7z

1112??....?? x?10(x?1)(x?2)(x?9)(x?10)5

?xy?x?x?y?1?2

??xz?2x?3解方程组?

?x?z?2

?(y?1)(z?2)?y?z?3?4

?

a2b2c2

a+b+c=0这3个数均不为0求2 ?2?22a?bc2b?ac2c?ab

xyztx?yy?zz?tt?x求 ??????y?z?tz?t?xt?x?yx?y?zz?tt?xx?yy?z

a?

111221?1,b??1求c? x??1,y??1求z? yzbcax

2x?3xy?2y511abcda?b?c?d ?求? ???求x?4xy?y8xybcdaa?b?c?d

ba?c?ba?b?c7a?b28求 已知a?a?1?0求a?4 ??a?bb?c?a2a?b?2ca?ba

a2b2111求2?2 ??aaba?bb

xyz=1,x+y+z=2, x?y?z?16求

222111 ??xy?2zyz?2xxz?2y

x2y2z2xyz?? ???1求y?zx?zx?yy?zz?xx?y

x+y=-1求x?5xy?xy?8xy?xy?5xy?y

43222234b?cc?aa?b222 ?????(a?b)(a?c)(b?c)(b?a)(c?a)(c?b)a?bb?cc?a

x3x2n ??....?(x1?x2?x3?...?xn?1)(x1?x2?x3?...?xn)x1(x1?x2)(x1?x2)(x1?x2?x3)

=

x2?....?xn x1(x1?...?xn)

xyyzxzxyz1?a?b,?a,?a?b,?求a x?yy?zx?zx?y?z12

a+b=1求证

abc???0 (bc?a2)2(ac?b2)2(ab?c2)2

a3b3c3(a?b?c)3abc ??求证2?2?2?2xyz(x?y?z)xyz

a+b=3,ab=1,c+d=4,cd=2且abcd????B b?c?dc?d?aa?b?da?b+c

a2b2c2d2

????7B?7 求证b?c?dc?d?aa?b?da?b+c

a3b3c3d3

????49B?68 b?c?dc?d?aa?b?da?b+c

3333

q11111 p,q互质且为正整数求证p为1979的倍数 ?1????...??p23413181319

b2?c2c2?a2a2?b2

?? （x-36）(x-144)-1991是完全平方数求x ??abc

a2?b2?1求证

ba2(b?a) ??a?1b?1a?b?1

x+y+z=x?y?z?2求证

222xy ?22(1?y)(1?x)a?bb?cc?a,q=,r=求证（1+p）(1+q)(1+r)=(1-p)(1-q)(1-r) a?bb?cc?a

abc?1,a?b?c?2,a2?b2?c2?3求

111 ??ab?c?1bc?a?1ac?b?1

(x?2)4?(x?1)2?1 x?5x?2005?0求(x?1)(x?2)2

(a?b?c)3(b?c?a)3(c?a?b)3(a?b?c)3

x2y2z2

x+y+z=0，???0求证a2x?b2y?c2z?bcx?acy?abz b?cc?aa?b

x?

1117?4,y??1,z??求xyz yzx3

a4?ma2?11a?4a?1?0,3?3求 22a?ma?2am2

c2a2bd??1 a+c=?dx,a-c=?bx,a?b求证(b?d)2(b?d)2xx

a1?a2???an?n3，

111?????． a2?1a3?1a100?1

(1?a)2(1?b)2

1?x2

1111设S＝3＋3＋3＋?＋，则4S的整数部分为多少？ 31232011