设a>0,试问a取何值时y=a+1/a-根号a^2+1/a^2+1的值最大,最大值是多少
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/20 18:25:51
![设a>0,试问a取何值时y=a+1/a-根号a^2+1/a^2+1的值最大,最大值是多少](/uploads/image/z/13002425-17-5.jpg?t=%E8%AE%BEa%3E0%2C%E8%AF%95%E9%97%AEa%E5%8F%96%E4%BD%95%E5%80%BC%E6%97%B6y%3Da%2B1%2Fa-%E6%A0%B9%E5%8F%B7a%5E2%2B1%2Fa%5E2%2B1%E7%9A%84%E5%80%BC%E6%9C%80%E5%A4%A7%2C%E6%9C%80%E5%A4%A7%E5%80%BC%E6%98%AF%E5%A4%9A%E5%B0%91)
设a>0,试问a取何值时y=a+1/a-根号a^2+1/a^2+1的值最大,最大值是多少
设a>0,试问a取何值时y=a+1/a-根号a^2+1/a^2+1的值最大,最大值是多少
设a>0,试问a取何值时y=a+1/a-根号a^2+1/a^2+1的值最大,最大值是多少
a=1时Ymax=2-√3
设x=a+1/a(a>0),则x>=2,√(x^2-2)>=√2,
∴a+1/a-√(a²+1/a²)
=x-√(x^2-2)
=2/[x+√(x^2-2)]
<=2/(2+√2)
=2-√2.