已知a^2+4a+(a+b)^2+10(a+b)+29=0.求3a^2-(a^2b-(3ab-a^2 乘b）-4a^2)-2ab的值

题目

已知a^2+4a+(a+b)^2+10(a+b)+29=0.求3a^2-(a^2b-(3ab-a^2 乘b）-4a^2)-2ab的值

答案

a^2+4a+(a+b)^2+10(a+b)+29=0
(a+2)²+(a+b+5)²=0
∴a+2=0
a+b+5=0
∴a=-2
b=-3
3a^2-(a^2b-(3ab-a^2 乘b）-4a^2)-2ab
=3a²-a²b+3ab-a²b+4a²-2ab
=7a²-2a²b+ab
=7*(-2)²-2*(-2)²*(-3)+(-2)*(-3)
=28+24+6
=58