\(G=\sqrt{a-4+4\sqrt{a-4}+4}+\sqrt{a-4-4\sqrt{a-4}+4}\)
\(=\sqrt{\left(\sqrt{a-4}+2\right)^2}+\sqrt{\left(\sqrt{a-4}-2\right)^2}\)
\(=\sqrt{a-4}+2+\sqrt{a-4}-2=2\sqrt{a-4}\)
\(G = \sqrt{a + 4 \sqrt{a – 4}} + \sqrt{a – 4\sqrt{a – 4}} \) \(= \sqrt{a – 4 + 4 + 4\sqrt{a – 4}} + \sqrt{a – 4 + 4 – 4\sqrt{a – 4}}\)
\(= \sqrt{\sqrt{a - 4}^2 + 2^2 + 4\sqrt{a – 4}} + \sqrt{\sqrt{a - 4}^2 + 2^2 - 4\sqrt{a – 4}}\)
\(= \sqrt{(\sqrt{(a – 4)} + 2)^2} + \sqrt{(\sqrt{(a – 4)} - 2)^2}\)
\(= \sqrt{a – 4} + 2 +|\sqrt{a – 4} – 2|\)
+) Với \(4 < a < 8 ⇔ 0 < a – 4 < 4 ⇔ \sqrt{0} < \sqrt{a – 4} < \sqrt{4} ⇔ 0 <\sqrt{a – 4} < 2 \)
Do đó, ta có: \(G = \sqrt{a – 4} + 2 + 2 - \sqrt{a – 4} \) (vì \(2 > \sqrt{a – 4}\))
\(=4\)
➤Với \(4 < a < 8 \) thì \(G = 4 \)
1 like cho Ng.Hữu Minh và nhiều like cho H.Việt Tân.