作业帮设x>=1,y>=1,证x+y+1/xy
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/28 07:12:26
设x>=1,y>=1,证x+y+1/xy
设x>=1,y>=1,证x+y+1/xy<=1/x+1/y+xy.
设x>=1,y>=1,证x+y+1/xy
证明：因为x≥1,y≥1,所以(xy－1)(x－1)(y－1)≥0,
展开得x^2y^2－x^2y－xy^2＋x＋y－1≥0,移项得：x^2y＋xy^2＋1≤x^2y^2＋x＋y.
两边同除以xy得x＋y＋1/xy≤1/x＋1/y＋xy
x+y+1/xy=(x^2y+xy^2+1)/(xy)
1/x+1/y+xy=(y+x+x^2y^2)/(xy)
y+x+x^2y^2-(x^2y+xy^2+1)=（xy-1)(x+y-1)>=0
因此x+y+1/xy=(x^2y+xy^2+1)/(xy)＜＝(y+x+x^2y^2)/(xy)＝1/x+1/y+xy
因式分解（x+y-2xy)(x+y-2)+(xy-1)^2设x+y=a,xy=b,
设f(x,y)=xy+x/y,则f(x+y,1）=（ ）
设x,y为正整数,且xy-(x+y)=1,则xy的最小值?
设xy都是正数,且xy-(x+y)=1,则x+y取值范围
设x>=1,y>=1,证x+y+1/xy
设x>=1,y>=1,证x+y+1/xy
设x大于等于1,y大于等于1.说明x+y+1/xy=1/x+1/y+xy
设X,Y属于正实数,xy-(x+1)=1,则x+y最小值
设X>=1 Y>=1证明X+Y+1/XY
1/x-1/y=x,求5y+xy-5y/y-xy-x=?
Z=x*sin xy+e^x+y或设y=(x)是由方程xy+sin x+sin y=1确定,求y”
设X.Y是实数,且X+Y=1,则XY的最大值着急、
xy>0,证xy+1/xy+x/y+y/x>=4
设方程3^（xy)=x+y+1确定的隐函数为y=y(x),求y'(0).
设x=【1/3】y,求【3y/x+3y】+【x/3y-x】-【6xy/9y²-x²】的值.
设xy满足约束条件 x+y>=1 x-2y>=-2 3x-2y
设实数x,y满足x^2+2xy+4y^2=1,则x+2y最大值
设x,y属于（0,正无穷）,且xy-(x+y)=1,求x+y的最小值