已知x+0+y+0+x+3y+xy+9

项饲腾1867(1)已知x(x+1) - (x^2+y)=3,求x^2+y^2\2 - xy的值 (2)已知x^2 - 3x+1=0,求x^4+1\x^4 -
昌何韩15946755087 ______ (1)已知x(x+1)-(x^2+y)=3 x^2+x-x^2-y=3 x-y=3 x^2-2xy+y^2=9 x^2-2xy+y^2=9 x^2+y^2\2-xy=9/2 (2)已知x^2-3x+1=0 x=3+√9-4*1/2=3+√5/2 或x=3-√9-4*1/2=3-√5/2 (1)x=3+√5/2 x^4+1\x^4=(3+√5/2)^4+1\(3+√5/2)^4=1\16(3+√5)^4+16\(3+√5)^4=1\...

项饲腾1867已知函数X≥0,Y≥0,求证X(5次方)+Y(5次方)≥X³Y²+X²Y³.. -
昌何韩15946755087 ______[答案] x^5+y^5-x^3y^2-x^2y^3=x^3(x^2-y^2)-y^3(x^2-y^2)=(x^2-y^2)(x^3-y^3)=(x+y)(x-y)(x-y)(x^2+xy+y^2)=(x-y)^2(x+y)(x^2+y^2+xy)因为x>=0,y>=0所以x+y>=0 x^2+y^2+xy>=0 (x-y)^2>=0所以x^5+y^5-x^3y^2-x^2y^3>=0即x^5...

项饲腾1867已知x的平方+xy+y的平方=0,则x分之y加y分之x等于? -
昌何韩15946755087 ______[答案] x的平方+xy+y的平方=0 x的平方+y的平方=-xy x/y+y/x=-1 如追加其它问题,采纳本题后点击想我求助,

项饲腾1867已知x,y,z>0,求证:已知x,y,z>0,求证:(x+y+z)(1/(x+y)+1/(y+z)+1/(z+x))≥9/2 ,用均值不等式解答! -
昌何韩15946755087 ______[答案] 由题.(x+y+z) (1/(x+y)+1/(y+z)+1/(z+x))= 1+ z/x+y +1 + x/y+z +1 + y/z+x = 3+ 3 (开3次方)√ xyz /(x+y)(y+z)(x+z) ≥3 + 3 (开3次方)√ xyz /8xyz = 3+ 3x1/2 =9/2 当且仅当 x=y=z 时成立

项饲腾1867已知x>0,y>0,3/(2+x)+3/(2+y)=1,求x+3y的最小值 -
昌何韩15946755087 ______[答案] 3/(2+x)+3/(2+y)=1 ,x>1,y>1 通分得:3(4+x+y)=(x+2)(y+2) xy-x-y-12=0 y=(x+12)/(x-1) x+3y=x+3(x+12)/(x-1) = [x(x-1)+3(x+12)]/(x-1) = (x²+2x+36)/(x-1) = (x²-2x+1+4x-4+39)/(x-1) = (x-1) + 39/(x-1) + 4 ≥ 2√39 + 4

项饲腾1867已知x>0, xy+y - 2=0,求y+y的最小值及相应的x,y的值
昌何韩15946755087 ______ XY+Y-2=0 y(x+1)-2=0 y=2/(x+1) x+y=x+2/(x+1) =x+1+2/(x+1) =【根号下(x+1)+1/根号下(x+1)]^2-2>=-2 所以它的最小值是-2, 此时根号下(x+1)=1/根号下(x+1) x=0,y=2/(x+1)=2

项饲腾1867已知x^2 - 7xy+12y=0,且x.y不等于0,求x^2 - 2xy+y^2/2xy的值 -
昌何韩15946755087 ______ x^2-7xy+12y=0,且x.y不等于0(x-3y)(x-4y)=0 x=3y 或x=4y(x^2-2xy+y^2)/(2xy)=(x-y)^2/(2xy) x=3y时 原式=4y^2/(6y^2)=2/3 当x=4y时 原式=9y^2/(8y^2)=9/8 如果你认可我的回答,请点击左下角的“采纳为满意答案”,祝学习进步!

项饲腾1867已知x+y+z=0,x2+y2+z2=1,求xy+yz+xz,x4+y4+z4的解数字为平方和四次方, -
昌何韩15946755087 ______[答案] (x+y+z)^2=[(x+y)+z]^2 =(x^2+2xy+y^2)+z^2+2zx+2zy =x^2+y^2+z^2+2xy+2xz+2yz =x^2+y^2+z^2+2(xy+xz+yz)=0 x+y+z=0 xy + xz+yz= -1/2 (xy+xz+yz)^2 =x^2y^2+x^2z^2+y^2z^2+2xzy^2+2yzx^2+2xyz^2 =x^2y^2+x^2z^2+y^2z^2 +2xyz(x+y+z) =1/4 x^2y^2+x^2z^...

项饲腾1867已知(x+2)^2+|x+y+5|=0,求3x^2y - [2x^2y - (2xy - x^2y) - 4x^2] - xy -
昌何韩15946755087 ______[答案] (x+2)^2+|x+y+5|=0, x+2=0,x+y+5=0 x=-2,y=-3 3(x^2)y-2(x^2)y+2xy-(x^2)y+4x^2-xy =4x^2+xy =4*(-2)^2+(-2)*(-3) =16+6 =22

项饲腾1867已知2x+y=1,x大于0,y大于0 xy的求最大值下面这个是错解 为什么因为x大于0y大于0所以xy小于等于(2分之(x+y))的2次方 均值不等式解方程组得2x+y=1 ... -
昌何韩15946755087 ______[答案] (2x)*(y)小于等于(2x+y)/2的平方=1/4 等号成立当且仅当2x=y即x=1/4,y=1/2 所以xy小于等于1/8 错解法错的原因在于均值不等式应用时,两数之和为定值才能像错解中那样用