1、x=0,m=2,n=1带入,0=x^2-3x+2 ,得x=1或x=2 B(1,0)A(2,0)
2、B(n,0),A(m,0),BC=Vn^2+1,AC=Vm^2+1
AB=m-n,AB^2=m^2+n^2-2mn,mn=-1,AB^2=m^2+n^2+2
BC^2+AC^2=n^2+1+m^2+1+m^2+n^2+2=AB^2
∠ABC=90度
3、三种情况,BC=AC时,n^2+4n^2=4+4n^2, n=2或-2,n=2舍,n=-2
AB=AC,(2-n)^2=4+4n^2 ,n=-3/4或n=0 n=0舍,n=-3/4
BC=AB, n^2+4n^2=(2-n)^2, x=(-1±√5)/2
1、证明,翻折=>∠ABE=∠MBE=1/2∠ABM,∠NDF=∠CDF=1/2∠NDC
ABCD为矩形,BD为对角线=>∠ABM=∠NDC,∠DBC=∠ADB
又∠MBE=∠NDF,∠DBC=∠ADB=>∠MBE+∠DBC=∠ADB+∠NDF=>∠EBC=∠ADF
∠MBE=∠NDF,∠DBC=∠ADB=>180度- ∠MBE-∠ADB=180度-∠NDF-∠DBC
=>∠BED=∠BFD
∠BED=∠BFD,∠EBC=∠ADF,两组对角分别相等的四边形是平行四边形
=>BFDE为平行四边形
2、菱形=>∠CBD=∠EBD=∠ABE=30=>AE=2/V3=>DE=BE=4/V3
=>面积=4/V3*2=8V3/3
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