Question

1.已知x²+3x+1=0,求x²+1/x²的值

2.1/4x-2x²，1/x²-4 通分
3.x/x²-x-2,1/x-2 通分

Answer 1

1.已知x²+3x+1=0,求x²+1/x²的值
x²+3x+1=0
x+3+1/x=0 两边除以x
∴x+1/x=-3
两边平方得
(x+1/x)²=9
x²+2+1/x²=9
∴x²+1/x²=7

2.1/4x-2x²，1/x²-4 通分

最简公分母是2x(x+2)(x-2)
∴1/(4x-2x²)=-1/2x(x-2)=-(x+2)/2x(x+2)(x-2)
1/(x²-4)=1/(x+2)(x-2)=2x/2x(x+2)(x-2)

3.x/x²-x-2,1/x-2 通分
最简公分母是(x+1)(x-2)
∴x/(x²-x-2)=x/(x+1)(x-2)
1/(x-2)=(x+1)/(x+1)(x-2)

Answer 2

1.
已知x²+3x+1=0
那么x+3+1/x=0
x+1/x=-3
(x+1/x)²=9
x²+2+1/x²=9
x²+1/x²=7

2.
1/(4x-2x²)=1/2x(2-x)
1/(x²-4)=1/(x+2)(x-2)
所以通分的结果是1/(4x-2x²)=-(x+2)/2x(x-2)(x+2)
1/(x²-4)=2x/2x(x-2)(x+2)

3.
x/(x²-x-2)=x/(x+1)(x-2)
1/(x-2)
所以通分的结果是x/(x²-x-2)=x/(x+1)(x-2)1/(x-2)=(x+1)/(x+1)(x-2)