Question

a的平方加5b的平方加c的平方减2ab减4b加6c加10等于0

Answer 1

a^2+5b^2+c^2-2ab-4b+6c+10

=a^2-2ab+b^2+4b^2-4b+c^2+6c+10

=(a-b)^2+4(b^2-b+1/4-1/4)+(c^2+6c+9-9)+10

=(a-b)^2+4(b-1/2)^2-1+(c+3)^2-9+10

=（a-b）^2+4(b-1/2)^2+(c+3)^2=0

要使式子成立,则a-b=0

b-1/2=0

c+3=0

则a=b=1/2,c=-3

所以a+b+c=1/2+1/2-3=-2