Question

dem ca : x la a puterea a 2a +x+1 >0 ,oricare ar fi x real

Answer 1

x²+x+1>0⇔x²+2·x·1/2+(1/2)²-(1/2)²+1>0⇔(x+1/2)²+1-1/4>0⇔  (x+1/2)²+4/4-1/4>0⇔(x+1/2)²+3/4>0  ;  (x+1/2)²>0 si 3/4>0 pentru ∀ x∈R