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解：令$\frac{3}{8}x - 18 = m，$則$a = m - 2，$$b = m，$$c = m + 2。$
$\begin{aligned}&a^{2}+b^{2}+c^{2}-ab - ac - bc\\=&(m - 2)^{2}+m^{2}+(m + 2)^{2}-m(m - 2)-(m - 2)(m + 2)-m(m + 2)\\=&m^{2}-4m + 4+m^{2}+m^{2}+4m + 4-(m^{2}-2m)-(m^{2}-4)-(m^{2}+2m)\\=&m^{2}-4m + 4+m^{2}+m^{2}+4m + 4 - m^{2}+2m - m^{2}+4 - m^{2}-2m\\=&12\end{aligned}$
解：因?yàn)?a - b = 1，$$b - c=-3，$
所以$a - b+(b - c)=a - c=-2。$
$\begin{aligned}&2(b - a)^{2}-3(b - c)^{2}+4(a - c)^{2}\\=&2\times(-1)^{2}\times(a - b)^{2}-3(b - c)^{2}+4(a - c)^{2}\\=&2\times1^{2}\times1-3\times(-3)^{2}+4\times(-2)^{2}\\=&2\times1 - 3\times9+4\times4\\=&2-27 + 16\\=&-9\end{aligned}$
解：因?yàn)?$a - b = b - c=\frac {3}{5}，$?
所以?$a - c=(a - b)+(b - c)=\frac {3}{5}+\frac {3}{5}=\frac {6}{5}。$?
所以?$(a - b)^2=\frac {9}{25}，$??$(b - c)^2=\frac {9}{25}，$?
?$(a - c)^2=\frac {36}{25}。$?
?$ $?即?$a^2+b^2-2ab=\frac {9}{25}，$??$b^2+c^2-2bc=\frac {9}{25}，$?
?$a^2+c^2-2ac=\frac {36}{25}。$?
所以?$a^2+b^2-2ab + b^2+c^2-2bc + a^2+c^2-2ac$?
?$=\frac {9}{25}+\frac {9}{25}+\frac {36}{25}=\frac {54}{25}。$?
所以?$2(a^2+b^2+c^2)-2(ab + bc + ac)=\frac {54}{25}，$?
所以?$-2(ab + bc + ac)=\frac {54}{25}-2=\frac {4}{25}。$?
?$ $?所以?$ab + bc + ac=-\frac {2}{25}。$?
解：?$ (1)①$?設(shè)?$223 = x，$?
則原式?$=x^2-(x + 1)(x - 1)$?
?$=x^2-(x^2-1)$?
?$=x^2-x^2+1 $?
?$= 1$?
?$ ②$?設(shè)?$3.456 = a，$?則?$2.456 = a - 1，$??$5.456 = a + 2，$?
?$1.456 = a - 2，$?可得：
?$ \begin {aligned}&3.456×2.456×5.456-3.456^3-1.456^2\\=&a×(a - 1)×(a + 2)-a^3-(a - 2)^2\\=&a^3+a^2-2a-a^3-a^2+4a - 4\\=&2a - 4\end {aligned}$?
把?$a = 3.456$?代入得原式?$=2×3.456-4 = 2.912。$?
?$ (2)$?設(shè)?$123456788 = x，$??$123456786 = y，$?則
?$M=(x + 1)y，$??$N=x(y + 1)。$?
?$ M - N=(x + 1)y-x(y + 1)=xy + y-xy - x=y - x，$?
因?yàn)?$y-x=123456786 - 123456788=-2<0，$?
所以?$M<N。$?
$(a + b)^{2}=a^{2}+2ab + b^{2}$
$(a - b)^{2}=a^{2}-2ab + b^{2}$
$4ab=(a + b)^{2}-(a - b)^{2}$
$-\frac{3}{2}$
解：?$(2)②$?因?yàn)?$ab=1，$?
所以?$8ab=8$?
因?yàn)?$(2a?b)2=(2a+b)2?8ab，$?
?$2a+b=3，8ab=8，$?
所以?$(2a?b)2=32?8=1.$?
?$(3)$?數(shù)字?$1\sim 9$?的和為
?$1 + 2+3+4+5+6+7+8+9 = 45。$?
?$ $?因?yàn)楦鬟吷系乃膫€(gè)數(shù)字的和都等于?$21，$?
所以?$21×3-45 = 18，$?
所以?$x + y+(x + y)=18，$?即?$x + y = 9。$?
?$ $?因?yàn)槊窟吽膫€(gè)數(shù)字的平方和分別記為?$A，$?
?$B，$??$C，$?滿足?$A + B + C = 411，$?且
?$1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2+9^2$?
?$=285。$?
?$ $?所以?$x^2+y^2+(x + y)^2=411 - 285，$?
即?$x^2+y^2+81 = 411 - 285，$?
所以?$x^2+y^2=45。$?
?$ $?因?yàn)?$(x + y)^2=x^2+2xy + y^2，$?
所以?$81=45 + 2xy，$?
所以?$xy = 18。$?
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