第1个回答 2010-07-19
x+y+z=0,z=-(x+y)
代入x^3+y^3+z^3=0
x^3+y^3-(x+y)^3
=x^3+y^3-x^3-3X^2y-3xy^2-y^3
=-3xy(x+y)
=3xyz=0
所以xyz=0
3a²+ab-2b²=(3a-2b)(a+b)=0
得3a=2b或a=-b
所以a/b-b/a-(a^2+b^2)/ab=a/b-b/a-a/b-b/a=-2b/a
当3a=2b时,-2b/a=-3;
当a=-b时,-2b/a=2
即b分之a-a分之b-ab分之a²+b²=-3或2
a²-3a+1=0
2a5-5a4+2a3-8a²+3a=(a²-3a+1)(2a^3+a^2+3a)=0本回答被提问者采纳
第2个回答 2010-07-19
1.xyz=0
解答如下:
x+y=-z
所以 x^3+y^3+3x^2y+3xy^2=-z^3
所以x^3+y^3+z^3+3x^2y+3xy^2=0(x^3+y^3+z^3=0)
所以 3x^2y+3xy^2=0
所以 3xy(x+y)=0 (x+y+z=0)
所以 -3xyz=0
推出 xyz=0
2.首先 a/b-b/a-(a^2+b^2)/ab=-2b/a;
又 3a^2+ab-2b^2=0
推出 (a+b)(3a-2b)=0;
a=-b 或者 3a=2b;
答案是 2或者-3;
3.答案为0;
解答:
2a^5-5a^4+2a^3-8a^2+3a=2a^3(a^2+1)-5a^4-8a^2+3a= (a^2+1=3a)
a^4-8a^2+3a=a^2(a^2-8)+3a= (a^2=3a-1)
a^2(3a-9)+3a=
3a(a^2-3a+1)=0
第3个回答 2010-07-19
(x+y+z)3=0
=> x3+y3+z3+3x2y+3x2z+3y2z+3y2z+3z2x+3z2y+6xyz=0
=> x2y+x2z+y2x+y2z+z2x+z2y+2xyz=0
=> (x3+x2y+x2z)+(y3+y2x+y2z)+(z3+z2x+z2y)+2xyz=x3+y3+z3=0
=> x2(x+y+z)+y2(x+y+z)+z2(x+y+z)+2xyz=2xyz=0
=> xyz=0