比较√2020-√2019与√2019-√2018的大小

学习 时间:2026-04-06 16:44:56 阅读:6477
比较根号2020减根号下2019与根号2019减根号2018的大小

最佳回答

不安的紫菜

无奈的咖啡豆

2026-04-06 16:44:56

√2020-√2019

=[(√2020-√2019)(√2020+√2019)]/(√2020+√2019)

=[(√2020)² -(√2019)² ]/(√2020+√2019)

=(2020-2019)/(√2020+√2019)

=1/(√2020+√2019)

同理得:

√2019-√2018=1/(√2019+√2018)

分子相同,分母越大,分数越小

∵√2020+√2019>√2019+√2018

∴√2020-√2019<√2019-√2018

最新回答共有2条回答

  • 悦耳的酒窝
    回复
    2026-04-06 16:44:56

    √2020-√2019

    =[(√2020-√2019)(√2020+√2019)]/(√2020+√2019)

    =[(√2020)² -(√2019)² ]/(√2020+√2019)

    =(2020-2019)/(√2020+√2019)

    =1/(√2020+√2019)

    同理得:

    √2019-√2018=1/(√2019+√2018)

    分子相同,分母越大,分数越小

    ∵√2020+√2019>√2019+√2018

    ∴√2020-√2019<√2019-√2018

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