1.a2+b2+c2-ab-ac-bc=1/2[(a-b)2+(b-c)2+(a-c)2]
2.由a-b=3/5,b-c=3/5,两式相加得a-c=6/5
再由第一题的结论,
ab+ac+bc=a2+b2+c2-1/2[(a-b)2+(b-c)2+(a-c)2]
=1-1/2(9/25+9/25+36/25)
=1-1/2(54/25)=1-27/25=-2/25
4..a2+b2+c2-ab-ac-bc=1/2[(a-b)2+(b-c)2+(a-c)2]
=3/2
5.X2-13X+1=0,两边同除X
得X+1/X=13
两边平方得:X^2+X+1/x^2=13^2-2=167
两边再平方得X^4+X+1/X^4=167^2-2
所以X4+1/X4的个位数字的值为7^2-2的个位数为9-2=7
6.X3+Y3=(x+y)(x2-xy+y2)
=(x+y)[(x+y)2-3xy]=(x+y){(x+y)2-3*(1/2)*[(x+y)2-(x2+y2)]}
=1*{1^2-(3/2)*[1^2-3]}
=1+3=4
7.由X=a2+b2+20.y=4(ab-a)，得a2+b2=20-X,2ab=2a+y/2
再(a-b)2≥0得a2+b2-2ab≥0,再简化a2+b2≥2ab
所以20-X≥2a+y/2
因式分解
1.X2n+Xn-1/9Y2+1/4
=X2n+2*(1/2)Xn+(1/2)2-(1/3Y)2
=[(Xn+(1/2)]2-(1/3Y)2
=[Xn+(1/2)+1/3Y][Xn+(1/2)-1/3Y]
2.X2+5XY+X+3Y+6Y2
=X2+5XY++6Y2+X+3Y
=(X+3Y)(X+2Y)+X+3Y
=(X+3Y)(X+2Y+1)
3.6X-6Y-9X2+18XY-9Y2-1
