`\qquad (2-\sqrt{3})^{x^2 +4x-14}\ge 7+4\sqrt{3}`
`<=>(2-\sqrt{3})^{x^2 +4x-14}\ge (2+\sqrt{3})^2`
`<=>(2-\sqrt{3})^2 .(2-\sqrt{3})^{x^2 +4x-14}\ge (2+\sqrt{3})^2 (2-\sqrt{3})^2`
`<=>(2-\sqrt{3})^{x^2 +4x-12}\ge [(2+\sqrt{3})(2-\sqrt{3})]^2`
`<=>(2-\sqrt{3})^{x^2 +4x-12}\ge (4-3)^2`
`<=>(2-\sqrt{3})^{x^2 +4x-12}\ge 1` $\quad(1)$
Vì `0<2-\sqrt{3}<1` nên:
`(1)=>x^2+4x-12\le log _{2-\sqrt{3}} 1`
`<=>x^2+4x-12\le 0`
`<=> -6 \le x \le 2`
Vậy tập nghiệm bpt là: `S=[-6;2]`
Đáp án $A$