证明: [tex=5.286x1.5]WS74gUb/4Ppm99z/vI5JzNJ47jP2C+hbwVvynnfRTQw=[/tex] 的充要条件是 [tex=4.5x1.357]U6R4KZ/ZA1xG3kNTBBaoT+FoCalf1qdbw+cLi+CQZSk=[/tex].
举一反三
- 证明：[tex=5.286x1.5]WS74gUb/4Ppm99z/vI5JzHPuV4aKC/UXbgoE6V2iYso=[/tex]，当且仅当[tex=4.5x1.357]tBZYcFY3CZI2ZZwP4Yrihw==[/tex]
- 设 [tex=15.643x1.357]v65YHbkDoTgF8OnwGE1MXRnD+kme4TLWCEVeSpAHoOm8qlmSHTOP9k+794E+denodVJ/G+ek30mlbl5zQktcVw==[/tex], 求证: [tex=4.357x1.5]xG3cKwxKGpeNouknGIIvTDY7Rx/drpPc8uBZfh1yLnw=[/tex] 的充要条件是 [tex=4.5x1.357]U6R4KZ/ZA1xG3kNTBBaoT+FoCalf1qdbw+cLi+CQZSk=[/tex].
- 设 [tex=10.286x1.5]t3Ufiz9JtZUZU0a+rggd75QO8in8t8AvSjCnhH77hQjXSiY64NzFqCUh4wRn3rmf[/tex], 其中 [tex=2.929x1.0]d/kPCBGO7NXKoPcTR6SOTg==[/tex] 为自然数. 又 [tex=6.5x1.5]YW6OJkpD4zR04YA5sUCS6QmQPhmfOIjulT8ZKByKvWE=[/tex] 求证: [tex=4.5x1.357]U6R4KZ/ZA1xG3kNTBBaoT+FoCalf1qdbw+cLi+CQZSk=[/tex].
- 设[tex=0.786x1.0]AOSTmhvIsOwsdZlGoks7dg==[/tex]是唯一分解整环,[tex=0.857x1.214]to/MrMoO1ux8UhZHnpEvBg==[/tex]是[tex=0.786x1.0]AOSTmhvIsOwsdZlGoks7dg==[/tex]的分式域, [tex=4.429x1.357]rY/lUAhmwPO+6lpLOBzEag==[/tex] 和 [tex=4.143x1.357]kXgGxCkXj3nQYhKZVzXepg==[/tex]的首项系数都为 1, 假设在 [tex=1.929x1.357]LvgbK12lxuuUi3aOakladA==[/tex]中 [tex=4.5x1.357]U6R4KZ/ZA1xG3kNTBBaoT+FoCalf1qdbw+cLi+CQZSk=[/tex], 证明: $[tex=4.714x1.357]OGArpVea1+mttUDf3ORMwAt8EGGbJ4clJ4oo9trKs8U=[/tex] 注 题中不必假定 [tex=1.857x1.357]fBOYuAIZ/H4m1Dx+my86tg==[/tex]的首项系数为[tex=0.786x1.0]ycpt7/PpiATqHUACAPCXCQ==[/tex]
- 判断下列命题是否为真：（1）[tex=3.643x1.357]/5abqJjwKZ1qr+6hsVFF5EBvfq3ggOFNlHMClz0h9nk=[/tex]（2）[tex=2.929x1.357]rGJpyjIjJpbcoBTWxP0Jiw==[/tex]（3）[tex=4.5x1.357]2wycHMoqU83MyEp17iBils58bR7YLuCTI2G9NVAdlfY=[/tex]（4）[tex=5.214x1.357]CTz2gu+IIm1GgNmYMGaduCRtA41wnW4WqwRWwEhq6aA=[/tex]（5）[tex=4.857x1.357]1DcE2BMMOaZhTuxR/mjgsboXxfg5ET59Dp4I/jjEDuw=[/tex]（6）[tex=4.643x1.357]BSryrsQYOvTP2hTWRu6t4nAuJwlSs4L9jaq70EpB+Us=[/tex]（7）若[tex=6.0x1.357]y0IZLUnBO88nR8WBZYvd7QXv5S1OMINV5cQNzPyiyAc=[/tex]，则[tex=3.429x1.357]1brfPwTkVVIX4GfoMIUskA==[/tex]（8）若[tex=7.643x1.357]MhLfJXZnhbXiB0x3oNtFzThV4Y1mJxe1VYr7PkJE/T6hmTD3WWp+UxbNwvUQ6DHk[/tex]，则[tex=4.143x1.357]LZUA94ISo1po5HWsOVeBCjo0rMvj7uw3bGw5HiZenrI=[/tex]