Đáp án:
Giải thích các bước giải:
$ 2.7^{x + 2} + 7.2^{x + 2} ≤ 351\sqrt{14^{x}}$
$ ⇔ 98.7^{x} - 351\sqrt{7^{x}.2^{x}} + 28.2^{x} ≤ 0$
$ ⇔ (2.7^{\frac{x}{2}} - 7.2^{\frac{x}{2}})(49.7^{\frac{x}{2}} - 4.2^{\frac{x}{2}}) ≤ 0$
$ ⇔ [(\dfrac{7}{2})^{\frac{x}{2}} - \dfrac{7}{2}].[(\dfrac{7}{2})^{\frac{x}{2}} - \dfrac{4}{49}] ≤ 0$
$ ⇔ \dfrac{4}{49} ≤ (\dfrac{7}{2})^{\frac{x}{2}} ≤ \dfrac{7}{2}$
$ ⇔ (\dfrac{7}{2})^{-2} ≤ (\dfrac{7}{2})^{\frac{x}{2}} ≤ (\dfrac{7}{2})^{1}$
$ ⇔ - 2 ≤ \dfrac{x}{2} ≤ 1$
$ ⇔ - 4 ≤ x ≤ 2 ⇔ x ∈ [- 4; 2] ⇒ a = - 4; b = 2$
$ ⇒ b - 2a = 2 - 2(- 4) = 10 ∈ (\sqrt{7}; 4\sqrt{10})$
