Fie expresia E(x)=(x+1)^2 +2(x-7)+1,unde x apartine numerelor reale
a) Aratati ca E(x)=(x-2)(x+6),pentru orice x apartine numerelor reale.
b) Calculati E(-1).
c) Aratati ca E(x) +16≥0, pentru orice x apartine nr reale.

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Răspunsuri

2014-11-10T23:10:32+02:00
E(x)=x²+2x+1+2x-14+1=x²+4x-12
x²+4x-12=0
Δ=4+48=64
x1=(-4+8)/2=2
x2=(-4-8)/2=-6
(x-2)(x+2) am explicat si pct.a
b) E(-1)=(-1+1)²+2(-1-7)+1=0²+2·(-8)+1=16+1=-15
c) E(x)+16≥0
x²+4x-12+16≥0
x²+4x+4≥0
(x+2)(x+2)≥0
x1=x2=-2
x∈[-2,+α]