已知整数x.y互为相反数,且(2x+y)(x+2y)与-1/25的倒数相等,试求x-y的值

问题描述:

已知整数x.y互为相反数,且(2x+y)(x+2y)与-1/25的倒数相等,试求x-y的值
为什么?

整数x.y互为相反数,即x=﹣y(2x+y)(x+2y)与-1/25的倒数相等,即(2x+y)(x+2y)=﹣25所以(2x+y)(x+2y)=(﹣2y+y)(﹣y+2y)=﹣y²=﹣25 y²=25 y=±5 x=﹣5和5所以x-y=5-(﹣5)=10或者x-y=﹣5-5=﹣1...