1+a+b+c=1 (1)
8+4a++2b++c=2 (2)
(2)-(1)得
3a+b=-6
故M-N=8³+64a+8b+c-(-5³+25a-5b+c)
=39a+13b+637
=13(3a+b)+637
=13*(-6)+637
=559
2. 由x²+y²+5/4=2x+y得
(x-1)²+(y-1/2)²=0
故x=1,y=1/2
∴x^y+y^x=1+1/2=3/2
3.由x²+y²/2+4≤xy+2y得
(x-y)²+1/4(y-4)²≤0
故x=y=4
4. 由题意得
2x^2+3xy-2y^2-x+8y-6=(x+2y+m)(2x-y+n)
2x^2+3xy-2y^2-x+8y-6= 2x^2+3xy-2y^2+(2m+n)x+(2n-m)y+mn
故2m+n=-1
2n-m=8
mn=-6
解得m=-2,n=3