Question

七年级数学题，快，加分

综合题
1.已知2的x-3平方=2分之1，求x+x^-1分之x^2-x^-2的值
2.已知x^2+y^2-6x+2y+10=0
求分式5x^2-7xy+2y^2分之3x^2-2xy-y^2

Answer 1

1.已知2的x-3平方=2分之1，求x+x^-1分之x^2-x^-2的值
2(x-3)²=1/2可知x-3=±1/2
x+x^-1分之x^2-x^-2=x-1/x
当x=3+1/2=7/2时，原式=7/2-2/7=45/14
当x=3-1/2=5/2时，原式=5/2-2/5=21/10

2.已知x^2+y^2-6x+2y+10=0
求分式5x^2-7xy+2y^2分之3x^2-2xy-y^2
5x^2-7xy+2y^2分之3x^2-2xy-y^2
=（5x-2y)(x-y)分之(3x+y)(x-y)
=(5x-2y)分之(3x+y)

x^2+y^2-6x+2y+10=0
(x-3)^2+(y+1)^2=0
x=3, y=-1
代入：5x-2y=15+2=17
3x+y=9-1=8
原式=17分之8