已知正数x,y,z满足x+y+z=1求证x^2/y+2z +y^2/z+2x +z^2/x+2y≥1/3_百度作业帮
已知正数x,y,z满足x+y+z=1求证x^2/y+2z +y^2/z+2x +z^2/x+2y≥1/3
已知正数x,y,z满足x+y+z=1求证x^2/y+2z +y^2/z+2x +z^2/x+2y≥1/3
方法①根据平均值不等式：x^2/(y+2z)+(y+2z)/9≥2√{[x^2/(y+2z)][(y+2z)/9]}=2x/3y^2/(z+2x)+(z+2x)/9≥2√{[y^2/(z+2x)][(z+2x)/9]}=2y/3z^2/(x+2y)+(x+2y)/9≥2√{[z^2/(x+2y)][(x+2y)/9]}=2z/3以上3式相加：x^2/(y+2z)+y^2/(z+2x)+z^2/(x+2y)+3(x+y+z)/9≥2(x+y+z)/3∵x+y+z=1∴x^2/(y+2z)+y^2/(z+2x)+z^2/(x+2y)≥1/3方法②利用柯西不等式：[x^2/(y+2z)+y^2/(z+2x)+z^2/(x+2y)][(y+2z)+(z+2x)+(x+2y)]≥(x+y+z)^2=1而显然：(y+2z)+(z+2x)+(x+2y)=3(x+y+z)=3∴x^2/(y+2z)+y^2/(z+2x)+z^2/(x+2y)≥1/3【以上两方法证明中等号成立的条件都是x=y=z=1/3】
..你是不是题目看错了啊
这个解不出来正数X,Y满足X的平方—Y的平方=2XY,求下(X—Y)/(X+Y)值_百度作业帮
正数X,Y满足X的平方—Y的平方=2XY,求下(X—Y)/(X+Y)值
正数X,Y满足X的平方—Y的平方=2XY,求下(X—Y)/(X+Y)值
x^2-2xy+y^2=2*y^2(x-y)^2=(√2*y)^2x-y=√2*yx=(√2+1)y代入式子得结果=√2/(√2+2)=√2-1
X的平方-Y的平方-2XY=0x=(1+根2)y(X—Y)/(X+Y)=根2-1
（X+Y)*(X-Y)=2XY两边同时除以(X+Y)的平方，得到(X-Y)/(X+Y)=2XY/(X+Y)(X+Y)=2XY/(XX+2XY+YY)----（式子1）因为XX-YY=2XY,所以YY+2XY=XX----（式子2）把（式子2）代入（式子1），得到(X-Y)/(X+Y)=2XY/（XX+XX)=2XY/2XX=Y所以答案是Y/X。
X*X-Y*Y=2XY;X*X-Y*Y-2XY=0;X*X-2XY+Y*Y-2Y*Y=0;(X-Y)*(X-Y)-2Y*Y=0可以得出(X-Y-√2Y)*(X-Y+√2Y)=0;因为 X和Y都是正数;所以可以得出X=(1+√2)Y;因为(X—Y)/(X+Y)=(X*X+Y*Y-2XY)/(X*X-Y*Y)=2Y*Y/2XY=Y/X;所以可以得出答案:(X—Y)/(X+Y)=√2-1.正数x,y满足x平方—y平方=2xy,则（x-y）/(x+y)=?_百度作业帮
正数x,y满足x平方—y平方=2xy,则（x-y）/(x+y)=?
正数x,y满足x平方—y平方=2xy,则（x-y）/(x+y)=?
由X^2-Y^2=2XY可得X^2=2XY+y^2原式=/^2=/x^2=2xy/x^2=2y/x
(x-y)/(x+y)=[(x-y)(x-y)]/[(x+y)(x-y)]=(x^2+y^2-2xy)/(x^2-y^2)=(x^2+y^2-x^2+y^2)/2xy=(2y^2)/(2xy)=y/x您还未登陆，请登录后操作！
正实数x、y满足x+3y^2=12,求xy^6的最大值.
由均值不等式，
12=x+3y^2&=4(x*y^2*y^2*y^2)^(1/4),
∴xy^6&=3^4=81,
当x=y^2=3时取等号，
∴xy^6的最大值是81.
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大家还关注正数x，y满足x平方-y平方=2xy，求x-y除以x+y的值_百度作业帮
正数x，y满足x平方-y平方=2xy，求x-y除以x+y的值
正数x，y满足x平方-y平方=2xy，求x-y除以x+y的值
分别将俩求的式子平方.再将原x方-y方带入,由于是正数.结果分别为根号y和根号x}