已知XY-2的绝对值与Y-1的绝对值互为相反数,试求代数式的值xy分之二+(x+1)(y+1)分之二+(x+2)(y+2)分之二+……(x+2012)(y+2012)分之二通俗易懂些)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/05 20:18:10
![已知XY-2的绝对值与Y-1的绝对值互为相反数,试求代数式的值xy分之二+(x+1)(y+1)分之二+(x+2)(y+2)分之二+……(x+2012)(y+2012)分之二通俗易懂些)](/uploads/image/z/1660361-41-1.jpg?t=%E5%B7%B2%E7%9F%A5XY-2%E7%9A%84%E7%BB%9D%E5%AF%B9%E5%80%BC%E4%B8%8EY-1%E7%9A%84%E7%BB%9D%E5%AF%B9%E5%80%BC%E4%BA%92%E4%B8%BA%E7%9B%B8%E5%8F%8D%E6%95%B0%2C%E8%AF%95%E6%B1%82%E4%BB%A3%E6%95%B0%E5%BC%8F%E7%9A%84%E5%80%BCxy%E5%88%86%E4%B9%8B%E4%BA%8C%2B%EF%BC%88x%2B1%29%28y%2B1%29%E5%88%86%E4%B9%8B%E4%BA%8C%2B%EF%BC%88x%2B2%29%28y%2B2%29%E5%88%86%E4%B9%8B%E4%BA%8C%2B%E2%80%A6%E2%80%A6%EF%BC%88x%2B2012%29%28y%2B2012%EF%BC%89%E5%88%86%E4%B9%8B%E4%BA%8C%E9%80%9A%E4%BF%97%E6%98%93%E6%87%82%E4%BA%9B%EF%BC%89)
已知XY-2的绝对值与Y-1的绝对值互为相反数,试求代数式的值xy分之二+(x+1)(y+1)分之二+(x+2)(y+2)分之二+……(x+2012)(y+2012)分之二通俗易懂些)
已知XY-2的绝对值与Y-1的绝对值互为相反数,试求代数式的值
xy分之二+(x+1)(y+1)分之二+(x+2)(y+2)分之二+……(x+2012)(y+2012)分之二
通俗易懂些)
已知XY-2的绝对值与Y-1的绝对值互为相反数,试求代数式的值xy分之二+(x+1)(y+1)分之二+(x+2)(y+2)分之二+……(x+2012)(y+2012)分之二通俗易懂些)
∵│xy-2│+│y-1│=0.
∴y-1=0,即y=1;
xy-2=0,x*1-2=0,x=2.
则2/xy+2/(x+1)(y+1)+2/(x+2)(y+2)+…+2/(x+2012)(y+2012)
=2/(1x2)+2/(2x3)+2/(3x4)+…+2/(2013x2014)
=2x[1/(1x2)+1/(2x3)+1/(3x4)+…+1/(2013x2014)]
=2x(1-1/2+1/2-1/3+1/3-1/4+…+1/2013-1/2014)
=2x(1-1/2014)
=2013/1007
已知已知XY-2的绝对值与Y-1的绝对值互为相反数
绝对值互为相反数,那么xy-2=0,y-1=0
得:xy=2,y=1 推出x=2
原代数式=2/2+2/(2x3)+2/(3x4)+.....+2/(2014x2013)
=2x(1+1/2-1/3+1/3-1/4+....+1/2013-1/2014)
=2x(1-1/2014)
=2013/1007