Question

如果实数a、b、c满足a+2b+3c=12，且a2+b2+c2=ab+ac+bc，则代数值a+b2+c3的值为_____

Answer 1

a^2+b^2+c^2=ab+bc+ac

2a^2+2b^2+2c^2=2ab+2bc+2ac

(a²-2ab+b²)+(a²-2ac+c²)+(b²-2bc+c²)=0

(a-b)²+(a-c)²+(b-c)²=0

所以a=b=c

因a+2b+3c=12

所以a=b=c=2

a+b^2+c^3

=2+4+8

=14