则代数式x2 y2 z2−xy−yz−zx的最小值为多少?
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∵x2+y2-6x-8y+25=0,∴(x-3)2+(y-4)2=0,∴x=3,y=4,当x=3,y=4时,原式=43-34=712.
(3x-4y+5xy)-(2x-3y)+5xy=3x-2x-4y+3y+5xy+5xy=x-y+10xy=3+4×10=43
(3x-4y+5xy)-(2x-3y)+5xy=3x-4y+5xy-2x+3y+5xy=(x-y)+10xy=3+50=53
y-x=3xyx-y=-3xy(x-2xy-y)/(2x-14xy-2y)=(-3xy-2xy)/(-3xy*2-14xy)=-5xy/(-20xy)=1/4
由x^2-xy=5(1)y^2+xy=-2(2)(1)+(2)得x^2-xy+xy+y^2=5-2即有x^2+y^2=3
∵1-8x≥0,8x-1≥0,∴x=18,y=12,∴代数式xy+yx+2-xy+yx−2=14+4+2-14+4−2=52-32=1.故选:B.
(1)A-2B=2x2+3xy+2y-1-2(x2−xy+x−12)=2x2+3xy+2y-1-2x2+2xy-2x+1=5xy+2y-2x,当x=y=-2时,A-2B=5xy+2y-2x=5×(-2
∵x+y=8,xy=7,∴原式=3xy-(x+y)+4=21-8+4=17.故答案为:17
x=y+3,则,x-y=3x²-2xy+y²=(x-y)²=3²=9(-2)²+(π-3)º-|-5|-(-1)的2013次方-(3分之1)
∵y-x=3xy∴x-y=-3xy∴(2x-14xy-2y)/(x-2xy-y)=[2(x-y)-14xy]/[(x-y)-2xy]=(-6xy-14xy)/(-3xy-2xy)=(-20xy)/(-
因为y=3xy+x,所以x-y=-3xy,当x-y=-3xy时,2x+3xy−2yx−2xy−y=2(x−y)+3xy(x−y)−2xy=2(−3xy)+3xy−3xy−2xy=35.
此题主要是把x-y用-3xy代替就可作了x-2xy-y/2x-14xy-2y=(-3xy-2xy)/2(x-y)-14xy=-5xy/(-6xy-14xy)=-5xy/-20xy=1/4
1/2x^2+xy+1/2y^2=1/2(x^2+2xy+y^2)=1/2(x+y)^2=1/2
因为xy/(x+y)=1/2所以x+y=2xy原式=3(x+y)-5xy/(-x-y+3xy)=3*2xy-5xy/(-2xy+3xy)=xy/xy=1
∵y=1−8x+8x−1+12中1-8x≥0,8x-1≥0,∴x=18,y=12代数式xy+ yx+2 =14+4+2 =254=52.故选C.
因为x,y都是整数,则两数相乘乘积为20,这两个数只能是x=20,y=1或者x=5和y=2.则y^x=1或者32
∵xy^2=20=5*2^2∴x=5;y=2∴y^x=2^5=32