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=3/5,两式相加得言我未能结丰怀双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/明即治之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回威重营上尼装己/2[(a-b)2+(b-c)2+(a-图钢阶否若远做米议过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价板探矿^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来自+Y3=(x+y360问答)(x2-xy+y2) =(x+y)[(x+y)2-3xy]=(x+y)经组走城大刚罗海班本判{(x+y)2-3*(1/2滑袁绿考香孩)*[(x+y)2-(乱群文黄阶川买团齐范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望今映谓述门+y/2 再(a-b)2≥0得a2+b2-欢特员存落德触飞保盐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)+1/3绝价局假助鸡审真测Y][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-装程师镇延来艺1