Question

Fie a,b,c ∈ R, astfel incat 2a²+3b²+c²+12a-12b+2c+31=0
Sa se calculeze ( a+b)^{2016} - ( b+c)^{2016} +( 2c-a)^{2016} .

Answer 1

2(a+3)^2+3(b-2)^2+(c+1)^2=0 => 

a= -3
b=  2
c= -1
=>( a+b)^{2016} - ( b+c)^{2016} +( 2c-a)^{2016}=
=1-1 +1=
=1