比较根号5减去根号4与根号6减去根号5的大小.
来源:学生作业帮 编辑:搜狗做题网作业帮 分类:数学作业 时间:2024/07/07 19:56:40
比较根号5减去根号4与根号6减去根号5的大小.
根号5减去根号4与根号6减去根号5,到底谁大?
根号5减去根号4与根号6减去根号5,到底谁大?
![比较根号5减去根号4与根号6减去根号5的大小.](/uploads/image/z/8095970-2-0.jpg?t=%E6%AF%94%E8%BE%83%E6%A0%B9%E5%8F%B75%E5%87%8F%E5%8E%BB%E6%A0%B9%E5%8F%B74%E4%B8%8E%E6%A0%B9%E5%8F%B76%E5%87%8F%E5%8E%BB%E6%A0%B9%E5%8F%B75%E7%9A%84%E5%A4%A7%E5%B0%8F.)
方法1.
根号5减去根号4=2.236-2=0.236
根号6减去根号5=2.449-2.236=0.213
所以根号5减去根号4大于根号6减去根号5
方法2.
√5-√4=(√5+√4)(√5-√4)/(√5+√4)=(5-4)/(√5+√4)=1/(√5+√4)
√6-√5=(√6+√5)(√6-√5)/(√6+√5)=(6-5)/(√6+√5)=1/(√6+√5)
√6+√5>√5+√4>0
所以1/(√6+√5)
根号5减去根号4=2.236-2=0.236
根号6减去根号5=2.449-2.236=0.213
所以根号5减去根号4大于根号6减去根号5
方法2.
√5-√4=(√5+√4)(√5-√4)/(√5+√4)=(5-4)/(√5+√4)=1/(√5+√4)
√6-√5=(√6+√5)(√6-√5)/(√6+√5)=(6-5)/(√6+√5)=1/(√6+√5)
√6+√5>√5+√4>0
所以1/(√6+√5)