已知a>0,b>0,2c>a+b求证(1)c^2>ab (2)c-√c^2-ab
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/29 01:19:07
![已知a>0,b>0,2c>a+b求证(1)c^2>ab (2)c-√c^2-ab](/uploads/image/z/388062-54-2.jpg?t=%E5%B7%B2%E7%9F%A5a%3E0%2Cb%3E0%2C2c%3Ea%2Bb%E6%B1%82%E8%AF%81%EF%BC%881%EF%BC%89c%5E2%3Eab+%282%29c-%E2%88%9Ac%5E2-ab)
已知a>0,b>0,2c>a+b求证(1)c^2>ab (2)c-√c^2-ab
已知a>0,b>0,2c>a+b求证(1)c^2>ab (2)c-√c^2-ab
已知a>0,b>0,2c>a+b求证(1)c^2>ab (2)c-√c^2-ab
(1) 4c^2>a^2+b^2+2ab≥2ab+2ab≥4ab
c^2>ab
(2)∵a+b0,b>0
∴a*a+a*b
(1) 4c^2>a^2+b^2+2ab>2ab+2ab=4ab
c^2>ab
(2)看不懂,把括号写出来啊
(1) 4c^2>a^2+b^2+2ab≥2ab+2ab≥4ab
c^2>ab
(2)∵a+b<2c, 且a>0,b>0
∴a*a+a*b即:a^2+ab<2ac
a^2+ab+c^2<2ac+c^2
a^2-2ac+c^2
即c^2-ab>0
∴-√(c^2-ab)