若a+b=1,ab=3/16,则(a-b)²=

(a-b)²=(a+b)²-4ab
=1-4*3/16
=1/4
原式=ab(a^2-2ab+b^2)
=ab(a^2+2ab+b^2-4ab)
=ab(a+b)^2-4ab
=-2*（2/3)²-4*(-2)
=-8/9+8
=64/9
证明：a^3+b^3+c^3
=(a+b)(a^2-ab+b^2)+c^3
=(a+b)^3-3ab(a+b)+c^3
=(a+b+c)^3-3c(a+b)(a+b+c)-3ab(a+b)
=(a+b+c)^3-3c(a+b)(a+b+c)-3ab(a+b+c)+3abc
=(a+b+c)[(a+b+c)^2-3c(a+b)-3ab]+3abc
=(a+b+c)(a^2+b^2+c^2+2ab+2bc+2ac-3ac-3bc-3ab)+3abc
=(a+b+c)(a^2+b^2+c^2-ab-ac-bc)+3abc
=0.5(a+b+c)(2a^2+2b^2+2c^2-2ab-2ac-2bc)+3abc
=0.5(a+b+c)[(a-b)^2+(b-c)^2+(c-a)^2]+3abc
=3abc
则0.5(a+b+c)[(a-b)^2+(b-c)^2+(c-a)^2]=0
则a=b=c,为正三角形
x²-1/2x-1/2
1 -½
×
1 1
所以x²-1/2x-1/2可化为（x-½）（x+1)