Ta có:
\(x^2+6x+15=x^2+2.x.3+9+6=\left(x+3\right)^2+6\ge6\)
=> Min = 6 khi x = -3
x2 + 6x + 15
= x2 +6x+9+6
= (x2+6x+9)+6
= (x+3)2 +6
do (x+3)2 ≥ 0 ∀ x
⇔ (x+3)2 +6 ≥ 6 ∀ x
=> min = 6 dấu "=" xảy ra khi
x+3=0 ⇔ x=-3
vậy min = 6 khi x=-3