已知x>y>0,求证x+1/(x-y)x>=3
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/21 02:42:25
已知x>y>0,求证x+1/(x-y)x>=3
![已知x>y>0,求证x+1/(x-y)x>=3](/uploads/image/z/16959259-19-9.jpg?t=%E5%B7%B2%E7%9F%A5x%3Ey%3E0%2C%E6%B1%82%E8%AF%81x%2B1%2F%28x-y%29x%3E%3D3)
利用三元均值不等式:a,b,c均为正实数,则 a+b+c>=3*(3次根号下abc),所以
x+1/[y(x-y)]
=(x-y)+y+1/[y(x-y)] (由三元均值不等式)
>=3*[3次根号下(x-y)*y*1/(y(x-y))]
=3
即 x+1/[y(x-y)]>=3.
x+1/[y(x-y)]
=(x-y)+y+1/[y(x-y)] (由三元均值不等式)
>=3*[3次根号下(x-y)*y*1/(y(x-y))]
=3
即 x+1/[y(x-y)]>=3.
已知x,y,z 大于0,x+y+z=2,求证 xz/y(y+z)+zy/x(x+y)+yx/z(z+x)大于等于2/3
已知x+y+z=1,求证x
已知x>0,y>0且x+y=1,求证根号(x+1/2)+根号(y+1/2)
已知x>y>0,xy=1,求证(x^2+y^2)/(x-y)≥2根号2
已知x,y∈R*,x+y=1,求证2/x+1/y≥3+2根号2
已知|3x-y|+|x+y|=0,求x-y除以x*y的值.
已知sin(x+y)=1,求证:tan(2x+y)+tany=0
已知sin(x+y)=1,求证:tan(2x+y)+tany=0
已知sin(x+y)=1,求证:tan(2x+3y)=tany
已知xyz属于R+,x+y+z=1,求证x^3/(y(1-y))+y^3/(z(1-z))+z^3/(x(1-x))大于
已知x,y,z满足xyz=1,求证x^3/(x+y)+y^3/(y+z)+z^3/(z+x)大于等于3
已知x,y,z都是正数,且xyz=1,求证:x^2/(y+z)+y^2/(x+z)+z^2/(x+y)≥3/2