过圆x2 y2=1外一点m2,3作这个圆的
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xy/x+y=1/3x+y=3xyx2y2/x2+y2=1/5(xy)²/[(x+y)²-2xy]=1/5(xy)²/[(3xy)²-2xy]=1/5(xy)&
m²-3m+1=0,左右同时除以m,可知m-3+1/m=0即m+1/m=3m²+1/m²=(m+1/m)²-2=3²-2=7
x^2=4y焦点(0,1)Y=1/4X²的焦点过直线交抛物线A(X1Y1)B(X2Y2),Y1+Y2=5A,B到准线的距离之和=y1+y2+2=7所以线段长度=7
x3次方y-2x2y2+xy3=xy(x²-2xy+y²)=xy(x-y)²=3x3²=27如果本题有什么不明白可以追问,再问:=xy(x2-2xy+y2)=x
(x+1)(x+3)(x-2)(x-4)+24=[(x+1)(x-2)][(x+3)(x-4)]+24=(x^2-x-2)(x^2-x-12)+24=(x^2-x-7+5)(x^2-x-7-5)+24
原式=x4+x3y+4x3y+x2y+4x2y2+4x2y2+xy2+4xy3+xy3+y4,=x3(x+y)+4x2y(x+y)+xy(x+y)+4xy2(x+y)+y3(x+y),=-x3-4x2
(2x4-4x3y-x2y2)-2(x4-2x3y-y3)+x2y2=2x4-4x3y-x2y2-2x4+4x3y+2y3+x2y2=2y3,因为化简的结果中不含x,所以原式的值与x值无关.
∵m²+2m+1=0∴m=-1∴m³+2m²+3m=-2
因为m2+m-1=0所以(m2+m-1)(m+1)=0展开就是m3+2m2-1=0故此m3+2m2+3=4注:m3是m的3次方,m2是m的平方!
过两点M1(3,-2,1)和M2(-1,0,2)的直线方向向量为:M1M2=(-4,2,1)(x-1)/(-4)=y/2=(z-2)/1
M1M2=(-3,4,-6)M1M3=(-2,3,-1)两向量叉乘得向量n(14,8,-1)这是平面的法向量,又因为平面经过M3,则方程为14x+8(y-2)-(z-3)=0
原式=2x2y-2xy2-[-3x2y2+3x2y+3x2y2-3xy2]=2x2y-2xy2+3x2y2-3x2y-3x2y2+3xy2=2x2y-3x2y-2xy2+3xy2+3x2y2-3x2y
设圆的方程为X^2+Y^2+DX+EY+F=0把三个点代进去,求出D,E,Y,就可以了.方程就是X^2+Y^2+2X+10Y-11=0
原式=[x3y2-x2y-x2y+x3y2]÷3x2y=(2x3y2-2x2y)÷3x2y=23xy-23;当x=3,y=-1时,原式=23×3×(-1)-23=-83.
(x-y)2=x2-2xy+y2=9,当x2+y2=13时,13-2xy=9,解得xy=2.当xy=2,x2+y2=13时,x3y-8x2y2+xy3=xy(x2-8xy+y2)=2×(13-8×2)
(2X²-2y²)-3(X²y²+X²)+3(X²y²+y²)=2x²-2y²-3x²y&
m2(m+4)+2m(m2-1)-3m(m2+m-1)=m3+4m2+2m3-2m-3m3-3m2+3m,=m2+m,当m=25时,原式=425+25=1425.