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曲线E:x2m+y2n=1(m>0,n>0)与正方形M:|x|+|y|...

(1)由x2m+y2n=1x+y=4,得(n+m)x2-8mx+16m-mn=0,△=64m2-4(m+n)(16m-mn)=0,化简,得4mn(m+n)-64mn=0,又m>0,n>0,∴mn>0,∴m+n=16.(2)由2|AB|=|CA|+|BD|,得3|AB|=42,即|AB|=423,由x2m+y2n=1y=x+b,得(m+n)x2+2bmx+mb2-...

(Ⅰ)点列{Bn}在斜率为6的直线上,有 bn+1?bn(n+1)?n=6?bn+1?bn=6故数列{bn}是公差为6的等差数列. (Ⅱ)由向量AnAn+1与向量BnCn共线,得直线AnAn+1与直线BnCn的斜率相等即kAnAn+1=kBnCn,∴an+1?an(n+1)?n=bn?0n?(n?1)=bn∴bn=an+1-an=b1+6...

∵x=2m+n+2和x=m+2n时,多项式x 2 +4x+6的值相等,∴二次函数y=x 2 +4x+6的对称轴为直线x= 2m+n+2+m+2n 2 = 3m+3n+2 2 ,又∵二次函数y=x 2 +4x+6的对称轴为直线x=-2,∴ 3m+3n+2 2 =-2,∴3m+3n+2=-4,m+n=-2,∴当x=3(m+n+1)=3(-2+1)=-3时,x 2...

∵x=2m+n+2和x=m+2n时,多项式x 2 +4x+6的值相等,∴二次函数y=x 2 +4x+6的对称轴为直线x= 2m+n+2+m+2n 2 = 3m+3n+2 2 ,又∵二次函数y=x 2 +4x+6的对称轴为直线x=-2,∴ 3m+3n+2 2 =-2,∴3m+3n+2=-4,m+n=-2,∴当x=3(m+n+1)=3(-2+1)=-3时,x 2...

解:①两个整数根且乘积为正,两个根同号,由韦达定理有,x1•x2=2n>0,y1•y2=2m>0, y1+y2=﹣2n<0, x1+x2=﹣2m<0, 这两个方程的根都为负根,①正确; ②由根判别式有: △=b2﹣4ac=4m2﹣8n≥0,△=b2﹣4ac=4n2﹣8m≥0, ∵4m2﹣8n≥0,...

m-n+2≠0, ——》2m+n+2≠m+2n, ——》2m+n+4≠m+2n+2, 多项式x^2+4x+6=(x+2)^2+2, 由题意知:(2m+n+4)^2+2=(m+2n+2)^2+2, ——》(2m+n+4)^2-(m+2n+2)^2=0 ——》2m+n+4+m+2n+2=0 ——》3(m+n+1)=-3, ——》多项式=(-3+2)^2+2=3。

y=-x²-2mx+2n+1=-(x+m)^2+m^2+2n+1 若 -1

∀ x∈A case 1: n=0 x=1∈B case 2: n=2m x=2n+1 =4m +1 ∈B case 3: n=2m-1 x=2n+1 =2(2m-1) +1 =4m -1 ∈B => ∀ x∈A => x∈B => A is subset of B ∀ x∈B x=4k±1 case 1: k=0 x=±1 = 2(1)+1 or 2(0)+1 => x∈A case 2: k=2m x=4k±1...

∵x=2m+n+2和x=m+2n时,多项式x2+4x+6的值相等,∴二次函数y=x2+4x+6的对称轴为直线x=2m+n+2+m+2n2=3m+3n+22,又∵二次函数y=x2+4x+6的对称轴为直线x=-2,∴3m+3n+22=-2,∴3m+3n+2=-4,m+n=-2,∴当x=6(m+n+1)=6(-2+1)=-6时,x2+4x+6=(-6)2+4×...

(xm+yn)(xm-yn)=(xm)2-(yn)2=x2m-y2n,正确,故答案为:×.

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