Question

若(a^3-3ab^2+2b^3)/(a+2b)+|a^2+3ab+2b^2-6|=0,则实数a的值为

Answer 1

(a^3-3ab^2+2b^3)/(a+2b)

=(a³-ab²-2ab²+2b³)/(a+2b)

=[a(a+b)(a-b)-2b²(a-b)]/(a+2b)

=[(a-b)(a²+ab-2b²)]/(a+2b)

=[(a-b)(a-b)(a+2b)]/(a+2b)

=(a-b)²

(a^3-3ab^2+2b^3)/(a+2b)+|a^2+3ab+2b^2-6|=0

(a-b)²+|a²+3ab+2b²-6|=0

则,a-b=0,且a²+3ab+2b²-6=0

由a-b=0,得a=b,

代入,a²+3ab+2b²-6=0,

a²+3a²+2a²-6=0

a²=1

解得a=±1