高手急救高一3道菜鸟数学题！！！！

Question

1，若x不等于0是x^2+xy+y^2=0,则(x^2+3xy+y^2)/(x^2+y^2)=？
2.因式分解：4x^4-13x^2+9
3.因式分解：（x^2-2x）^2-7(x^2-2z)+12
大虾帮帮忙啊~~~~

Answer 1

1,
x^2+xy+y^2=0 则
x^2+3xy+y^2
=（x^2+xy+y^2）+2xy
=0+2xy
=2xy

x^2+y^2
=（x^2+xy+y^2）-xy
=0-xy
=-xy

则
(x^2+3xy+y^2)/(x^2+y^2)
=2xy/-xy
=-2
-----------------------------
2,
4x^4-13x^2+9
=(x^2-1)(4x^2-9)
=(x-1)(x+1)(2x-3)(2x+3)
--------------------------
3,(楼主:z应改成x)
（x^2-2x）^2-7(x^2-2x)+12
=(x^2-2x-4)(x^2-2x-3)
=(x^2-2x-4)(x-3)(x+1)

参考资料：初中教材

Answer 2

1，若x不等于0是x^2+xy+y^2=0,则(x^2+3xy+y^2)/(x^2+y^2)=？
x^2+y^2=-xy
(x^2+3xy+y^2)/(x^2+y^2)=-2
2.因式分解：4x^4-13x^2+9
=(4x^2-9)(x^2-1)
=(2x+3)(2x-3)(x+1)(x-1)
3.因式分解：（x^2-2x）^2-7(x^2-2z)+12
大虾帮帮忙啊~~~~
=(x^2-2x-3)(x^2-2x-4)
=(x-3)(x+1)(x^2-2x-4)

Answer 3

分解x^2+xy-2y^2=0,（x+2y)(x-y)=0,x=-2y或 x=y
(x^2+3xy+y^2)/(x^2+y^2)
=「(x^2+xy-2y^2)+(2xy+3y^2)」/(x^2+y^2)
=(2xy+3y^2)/(x^2+y^2)
将x=-2y ，x=y分别代入 可得
原式＝－1/5或5/2