Question

已知a的平方加b的平方加c的平方减2倍a加b加c再加三等于零求a的立方加b的立方加c的立方减3倍abc的值

Answer 1

a^2+b^2+c^2+2(a+b+c)+3=0

a^2+2a+1+b^2+2b+1+c^2+2c+1=0

(a+1)^2+(b+2)^2+(C+1)^2=0

因为(a+1)^2>=0 (b+2)^2>=0 (C+1)^2>=0

所以(a+1)^2=(b+2)^2=(C+1)^2=0

a=b=c=-1

a^3+b^3+c^3-3abc=-1-1-1+3=0