xyz不等于0x+y+z不等于0,(y+z)/x=(z+x)/y=(x+y)/z求(y+z)(z+x)(x+y)/xyz若|ab-2|+(b-1)(b-1)=0求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+``````+1(a+2006)(b+2006)

Question

xyz不等于0 x+y+z不等于0,(y+z)/x=(z+x)/y=(x+y)/z 求(y+z)(z+x)(x+y)/xyz
若|ab-2|+(b-1)(b-1)=0 求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+``````+1(a+2006)(b+2006)

Answer 1

1.设x=y=z=1则原式=8
2:若|ab-2|+(b-1)(b-1)=0
ab=2
b=1
a=2
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+``````+1(a+2006)(b+2006)
=1/(2*1)+1/(3*2)+1/(4*3)+.+1/(2008*2007)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2007-1/2008)
=1-1/2008
=2007/2008