求函数y=(x四次方+2x²+1)/(x²+2)的最小值及相应的x值,我是将y化成(x²+1)²/x²+1+1,约去得3次开方,均值不等式这地方很多题型不会,
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![求函数y=(x四次方+2x²+1)/(x²+2)的最小值及相应的x值,我是将y化成(x²+1)²/x²+1+1,约去得3次开方,均值不等式这地方很多题型不会,](/uploads/image/z/6932642-50-2.jpg?t=%E6%B1%82%E5%87%BD%E6%95%B0y%3D%28x%E5%9B%9B%E6%AC%A1%E6%96%B9%2B2x%26%23178%3B%2B1%EF%BC%89%2F%EF%BC%88x%26%23178%3B%2B2%EF%BC%89%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E5%8F%8A%E7%9B%B8%E5%BA%94%E7%9A%84x%E5%80%BC%2C%E6%88%91%E6%98%AF%E5%B0%86y%E5%8C%96%E6%88%90%EF%BC%88x%26%23178%3B%2B1%EF%BC%89%26%23178%3B%2Fx%26%23178%3B%2B1%2B1%2C%E7%BA%A6%E5%8E%BB%E5%BE%973%E6%AC%A1%E5%BC%80%E6%96%B9%2C%E5%9D%87%E5%80%BC%E4%B8%8D%E7%AD%89%E5%BC%8F%E8%BF%99%E5%9C%B0%E6%96%B9%E5%BE%88%E5%A4%9A%E9%A2%98%E5%9E%8B%E4%B8%8D%E4%BC%9A%2C)
求函数y=(x四次方+2x²+1)/(x²+2)的最小值及相应的x值,我是将y化成(x²+1)²/x²+1+1,约去得3次开方,均值不等式这地方很多题型不会,
求函数y=(x四次方+2x²+1)/(x²+2)的最小值及相应的x值,
我是将y化成(x²+1)²/x²+1+1,约去得3次开方,均值不等式这地方很多题型不会,
求函数y=(x四次方+2x²+1)/(x²+2)的最小值及相应的x值,我是将y化成(x²+1)²/x²+1+1,约去得3次开方,均值不等式这地方很多题型不会,
令a=x²+1
则a≥1
所以y=a²/(a+1)
=(a²-1+1)/(a+1)
=(a²-1)/(a+1)+1/(a+1)
=a-1+1/(a+1)
=(a+1)+1/(a+1)-2
(a+1)+1/(a+1)看做对勾函数
则a+1>1时递增
这里a≥1,满足a+1>0
是递增的
所以a=1时
即x=0,最小值是2+1/2-2=1/2