幂的运算（过程已知a+b=1,a(a^2+2b)+b(-3a+b^2)=0.5,求ab

幂的运算（过程已知a+b=1,a(a^2+2b)+b(-3a+b^2)=0.5,求ab
幂的运算（过程
已知a+b=1,a(a^2+2b)+b(-3a+b^2)=0.5,求ab

幂的运算（过程已知a+b=1,a(a^2+2b)+b(-3a+b^2)=0.5,求ab
a(a^2+2b)+b(-3a+b^2)=0.5
a^3+2ab-3ab+b^3=0.5
a^3+b^3-ab=0.5
(a+b)(a^2-ab+b^2)-ab=0.5
a^2-ab+b^2-ab=0.5
a^2+b^2-2ab=0.5
(a^2+b^2+2ab)-4ab=0.5
(a+b)^2-4ab=0.5
1-4ab=0.5
4ab=0.5
ab=0.5/4=0.125

a(a^2+2b)+b(-3a+b^2)
=a^3+2ab-3ab+b^3
=(a^3+b^3)-ab
=(a+b)(a^2-ab+b^2)-ab
=(a+b)[(a+b)^2-3ab]-ab
a+b=1
原式=(1-3ab)-ab=1-4ab=0.5
4ab=0.5
ab=1/8

由a(a^2+2b)+b(-3a+b^2)=0.5得a^3-ab+b^3=0.5
(a+b)(a^2-ab+b^2)-ab=0.5
(a^2-ab+b^2)-ab=0.5
[(a+b)^2-3ab]-ab=0.5
1-4ab=0.5
ab=1/8

a^3+b^3+2ab-3ab=0.5
a^3+b^3-ab=0.5
(a+b)(a^2-ab+b^2)-ab=0.5
1*[(a+b)^2-3ab]-ab=0.5
1-4ab=0.5
ab=1/8