已知X Y分之一=Z X分之一=1,
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1/x-1/y=3等号左边通分,得(y-x)/(xy)=3故x-y=-3xy代入分式[2x+3xy-2y]/[x-2xy-y]=[2(x-y)+3xy]/[(x-y)-2xy]=(-6xy+3xy)/
这个比较简单了:由已知条件得:x+y=3xy那么:x-2xy+y=3xy-2xy=xy2x+3xy+2y=6xy+3xy=9xy所以答案是:9再问:x分之一+y分之一=3为什么等于x+y=3xy再答:
xy=11/x+1/y=2两边乘xyx+y=2两边平方x²+y²+2xy=4所以x²+y²=4-2xy=2所以原式=2(x²+y²)/x
(3x-5xy+3y)/(x+xy+y)分式上下同除xy,得,(3/y-5+3/x)/(1/y+1+1/x)=1/3再问:太给力了,你的回答完美解决了我的问题!
x分之一-y分之一=2005(y-x)/xy=2005y-x=2005xy2x+6016xy-2y分之-x+xy+y=[(y-x)+xy]/[6016xy-2(y-x)]=(2005xy+xy)/(6
=1-1/2-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-(1/5-1/6)=1-1+1/3-1/3+1/4-1/4+1/5-1/5+1/6=1/6
本题考查最值不等式:a+b≥2√ab当且仅当a=b时,取等号x√yz+y√zx+z√xy≤x(y+z)/2+y(z+x)/2+z(x+y)/2当且仅当y=z,z=x,x=y,即:x=y=z时,取等号,
1/2x²+xy+1/2y²=1/2(x²+2xy+y²)=1/2(x+y)²=1/2
由已知得:xy=-1,1/x-1/y=(y-x)/(xy)=5那么:y-x=5xy=-5所以:(y-x)²=25即:y²-2xy+x²=25得:y²+x
x+y=6两边同时平方得x²+2xy+y²=36把xy=-2代入上式得x²+y²=401/x²+1/y²=y²/(x²y
(x分之一加y分之一加z分之一)乘xy+yz+zx分之xy=(yz+xy+xz)/(xyz)*xy/(yz+xy+xz)=1/z
1/x+1/y=(x+y)/xy=4/3
因为(x+1/y)(y+1/x)=xy+1+1+1/xy=18+2=20所以y+1/x=20/5=4再问:哦再问:我没想到,,,,
1/x+1/y=(x+y)/xy=5x+y=5xy所以原式=[2(x+y)-3xy]÷[(x+y)+2xy]=[2(5xy)-3xy]÷[(5xy)+2xy]=7xy÷7xy=1再问:1/x+1/y=
3x-3y=xy3/x-3/y=1(两边同除xy)1/x-1/y=1/3
1/2x^2+xy+1/2y^2=8同乘以2x^2+2xy+y^2=16两边减去4xyx^2-2xy+y^2=16-4×3=4整理即得(x-y)^2=4
选择题最好的方法:设X=2,Y=1或X=-2,Y=-1,则1/X+1/Y=1/2+1=1.5或1/X+1/Y=-(1/2+1)=-1.5
xy:yz:zx=3:2:1xy:yz=3:2则x:z=3:2同理y:z=3:1=6:2故(x+y):z=(3+6):2=9:2
①x:y:z因为xy:yz:zx=3:2:1所以xy:yz=3:2所以x:z=3:2同理yz:zx=2:1所以y:x=2:1=6:3所以x:y:z=3:6:2②x/yz:y/zx=x^2:y^2=(x