b) $14m - 6m^2 - 13$
$=-6m^2 + 14m - 13$
$=-6m^2 + 14m - \dfrac{49}{6} - \dfrac{29}{36}$
$=-6\bigg(m^2 - \dfrac{7}{3}m + \dfrac{49}{36}\bigg) - \dfrac{29}{36}$
$=-6\bigg[m^2 - 2.m.\dfrac{7}{6} + \bigg(\dfrac{7}{6}\bigg)^2\bigg] - \dfrac{29}{36}$
$=-6\bigg(m - \dfrac{7}{6}\bigg)^2 - \dfrac{29}{36}$
Vì $ -6\bigg(m - \dfrac{7}{6}\bigg)^2 \leq 0 ∀ m$
nên $-6\bigg(m - \dfrac{7}{6}\bigg)^2 - \dfrac{29}{36} \leq -\dfrac{299}{36} < 0 ∀ m$
Hay $14m - 6m^2 - 13 \leq 0 ∀ m$
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b) $6b - b^2 - 10$
$=-b^2 + 6b - 9 -1$
$=-(b^2 - 2.b.3 + 3^2) - 1$
$=-(b-3)^2 - 1$
Vì $ -(b-3)^2 \leq 0 ∀ b$
nên $-(b-3)^2 - 1 \leq -1 < 0 ∀ b$
Hay $6b - b^2 - 10 < 0 ∀ b$
