根号 12x²y 24x²y³
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显然不等式两边都大于0平方后:x+y+2√xy≤a^2(x+y)整理下:(a^2-2)(x+y)+x+y-2√x≥0(a^2-2)(x+y)+(√x-√y)^2≥0若恒成立,显然需要满足(a^2-2)
解∵x+2y≥0∴√(x+2y)×√(2x+4y)=√2√(x+2y)²=√2(x+2y)
y=根号(x-8)+根号(8-x)+18,x-8≥0,8-x≥0x=8,y=18[(x+y)/(根号x+根号y)]-2xy/(x根号y-y根号x)=26/(2√2+3√2)-288/(8*3√2-18
题是这样的吧:[(√x-√y)^3+2x√x+y√y]/(x√x+y√y)+[3√(xy)-3y]/(x-y)原式=[(x√x-3x√y+3y√x-y√y)+2x√x+y√y]/(x√x+y√y)+[
设根号下x+y=a,则a平方+a=12可算出a1=-4,舍去a2=3所以x+y=9再和x+xy+y=23组成方程组,解得x1=7,y1=2x2=7y2=7
解题思路:根据非负数的行政列出方程求出x,y的值即可求出x²的值解题过程:
(x-y)/(√x-√y)=(x-y)(√x+√y)/[(√x-√y)(√x+√y)]=(x-y)(√x+√y)/(x-y)=√x+√y)(√12-√11)²-(√11-√10)²
当X,Y大于等于零时,根号X*Y等于根号X*根号y当X,Y小于零时,根号X*Y成立,根号X*根号y不存在
(x√x+x√y)/(xy-y^2)-[x+√(xy)+y]/(x√x-y√y)=[x(√x+√y)/[y(√x-√y)(√x+√y)]-[x+√(xy)+y]/{(√x-√y)[x+√(xy)+y]
高中的方法早忘了,给你介绍高数方法吧条件方程:x+y-12=0求最值方程:√(x^2+4)+√(y^2+9)则拉格朗日方程为L(x,y)=√(x^2+4)+√(y^2+9)+k(x+y-12)【k为某
(根号y/根号x-根号y)-(根号y/根号x+根号y)={根号y(根号x+根号y)}/(x-y)-{根号y(根号x-根号y)}/(x-y)=(y+y)/(x-y)因为x=2y所以原式=2y/y=2
√x+√y≤k√(x+y)平方得x+y+2√(xy)≤k²(x+y)∵2√(xy)≤x+y∴左≤2(x+y)恒成立,故有k²≥2,且显然k>0∴kmin=√2
原式=[(√x-√y)²+(√x+√y)²]/(√x+√y)(√x-√y)=(x+y-2√xy+x+y+2√xy)/(x-y)=2(x+y)/(x-y)=2(2+√3)/(2-√3
x^2-2xy+y^2-√3x-√3y+12=0,令x=m+n,y=m-n代入化简得:4n^2-2√3m+12=02n^2-√3m+6=02n^2=√3m-6,m>=2√3xy=m^2-n^2=m^2
((x-y)/(√x+√y))-(x+y-2√xy)/(√x-√y),分母有理化,第一个式子分母乘以√x-√y,又(x+y-2√xy)=(√x-√y)(√x-√y),所以原式等于√x-√y-(√x-√
原式=√y/(√2y-√y)-√y/(√2y+√y)=√y/[√y(√2-1)]-√y/[√y(√2+1)]=1/(√2-1)-1/(√2+1)=(√2+1)/(√2+1)(√2-1)-(√2-1)/
原式=-10/3√12x^2*3x/y*x/4y=-10x^2/y=-10/2=-5
可知x≥0,y≥0(x-y)/(√x+√y)-(x-2√xy+y)/(√x-√y)=(√x+√y)(√x-√y)/(√x+√y)-(√x-√y)²/(√x-√y)=(√x-√y)-(√x-√
6/√(x+y)÷12/√(x-y)=√(x-y)/[2√(x+y)]=√(x^2-y^2)/[2(x+y)]