请解决两道题如果a+b+c=0,1/a+1/b+1/c=-4,那么1/(a^2)+1/(b^2)+1/(c^2)的值是A.3B.8C.16D.20如果(x+1)(y+1)=x^2*y+x*y^2=6,那么x^2+y^2等于A.6B.5C.4D.3

Question

请解决两道题
如果a+b+c=0,1/a+1/b+1/c=-4,那么1/(a^2)+1/(b^2)+1/(c^2)的值是
A.3 B.8 C.16 D.20
如果(x+1)(y+1)=x^2*y+x*y^2=6,那么x^2+y^2等于
A.6 B.5 C.4 D.3

Answer 1

1、C.16
设X=1/a,Y=1/b,Z=1/c ；X+Y+Z=-4 ,
两边平方：XX+YY+ZZ+2（XY+YZ+XZ） =16 ；
1/X+1/Y+1/Z=0,两边乘XYZ,（XY+YZ+XZ）=0
1/(a^2)+1/(b^2)+1/(c^2)=XX+YY+ZZ=16
2、B.5
设A= X+Y,B =XY
(x+1)(y+1)= X+Y+XY+1=A+B+1=6
x^2*y+x*y^2= （X+Y）XY=AB=6
x^2+y^2= （X+Y）（X+Y）-2XY=AA-2B
A=2,B=3无解
A=3,B=2,x^2+y^2=5