Question

Determinati a si b stiind ca E(a+b+1) + E(a) + 2b = 0
E(x)=-x²
DAU COROANA!!!!!!!!!!!!

Answer 1

E(a+b+1)= -(a+b+1)^2 = -(a^2+b^2+1+2ab+2a+2b)
E(a)=-a^2

E(a+b+1)+E(a)+2b=2a^2+b^2+2ab+2a+1=(a^2+b^2+2ab)+(a^2+2a+1)=
=(a+b)^2 + (a+1)^2=0
avem suma de termeni pozitivi oricare ar fi a;b, deci suma e nula daca:
a= - 1
si a+b=0 ⇒ b=1