用反证法证明:已知a,b均为有理数,且https://bgk-photo.cdn.bcebos.com/8b82b9014a90f60329f732272912b31bb051ed0f.jpg和https://bgk-photo.cdn.bcebos.com/f9198618367adab42997b5239bd4b31c8701e40f.jpg都是无理数,求证:https://bgk-photo.cdn.bcebos.com/0b46f21fbe096b636d7cf0301c338744ebf8ac6d.jpg https://bgk-photo.cdn.bcebos.com/b999a9014c086e0669ef912b12087bf40ad1cb0f.jpg是无理数.
用反证法证明:已知a,b均为有理数,且https://bgk-photo.cdn.bcebos.com/8b82b9014a90f60329f732272912b31bb051ed0f.jpg和https://bgk-photo.cdn.bcebos.com/f9198618367adab42997b5239bd4b31c8701e40f.jpg都是无理数,求证:https://bgk-photo.cdn.bcebos.com/0b46f21fbe096b636d7cf0301c338744ebf8ac6d.jpg https://bgk-photo.cdn.bcebos.com/b999a9014c086e0669ef912b12087bf40ad1cb0f.jpg是无理数.
发布时间：2025-08-07 14:11:19
为有理数,则(
)(
-
)=a-b.由a>0,b>0,得
>0.∴
-
=
.∵a,b为有理数,且
为有理数.∴
为有理数,即
-
为有理数.∴(
) (
-
)为有理数,即2
为有理数.∴
应为有理数,这与已知
为无理数矛盾.∴
一定为无理数.
