1.计算(x-y+4xy/(x-y))(x+y-4xy/(x+y))2.已知x/(x^2-x+1)=7求x^2/(x^4+x^2+1)3.已知2x-3y+z=0,3x-2y-6z=0xyz≠0求(x^2+y^2+z^2)/(2x^2+y^2-z^2)4.解方程(x^2-x+1)/(x^2-x-1)=(x^2+x)/(x^2+x-2)23题为求值题要准确的数不要代数式

Question

1.计算 (x-y+4xy/(x-y))(x+y-4xy/(x+y))
2.已知x/(x^2-x+1)=7 求x^2/(x^4+x^2+1)
3.已知2x-3y+z=0,3x-2y-6z=0 xyz≠0 求(x^2+y^2+z^2)/(2x^2+y^2-z^2)
4.解方程 (x^2-x+1)/(x^2-x-1)=(x^2+x)/(x^2+x-2)
2 3题为求值题 要准确的数 不要代数式

Answer 1

1.={[(x-y)^2+4xy]/(x-y)}{[(x+y)^2-4xy]/(x+y)}
=[(x+y)^2/(x-y)][(x-y)^2/(x+y)]
={(x+y)/(x-y)}^3
2.由x/(x^2-x+1)=7 有
x=7x^2-7x+7
x+14x=7x^2-7x+7+14x
15x=7(x^2+x+1)
x/(x^2+x+1)=7/15
式子=x^2/(x^4+2x^2+1-x^2）
=x^2/[(x^2+1)^2-x^2]
=[x/(x^2-x+1)][x/(x^2+x+1)]
=7*7/15
=49/15
3.由2x-3y+z=0,3x-2y-6z=0有
y=3/4x
z=1/4x(把x当做已知数求2元2次方程)
y、z带入方程
原式=13/20(带入自己算应该会吧!)
4.原式可化为：
(x^2-x+1)(x^2+x-2)=(x^2+x)(x^2-x-1)
x^4-x^3-x^2+x^3-x^2-x=x^4-x^3+x^2+x^3-x^2+x-2x^2+2x-2
x^4-2x^2-x=x^4-2x^2+3x-2
解的x=1/2
(不知道有没有更好的解决方法,没去想...)