Question

Tìm x:

\(\sqrt{x+4\sqrt{x-4}}+\sqrt{x-4\sqrt{x-4}}=4\)

Mình cám ơn.

Answer 1

Answer 2

\(\sqrt{x+4\sqrt{x-4}}\) + \(\sqrt{x-4\sqrt{x-4}}\) = 4 (x \(\ge\) 8 )

<=> \(\sqrt{x-4+4\sqrt{x-4}+4}\) + \(\sqrt{x-4-4\sqrt{x-4}+4}\) = 4

<=> \(\sqrt{\left(\sqrt{x-4}+2\right)^2}\) + \(\sqrt{\left(\sqrt{x-4}-2\right)^2}\) = 4

<=> \(|\sqrt{x-4}+2|\) + \(|\sqrt{x-4}-2|\) = 4

<=> \(\sqrt{x-4}\) + 2 + \(|\sqrt{x-4}-2|\) = 4

+ TH1 \(\sqrt{x-4}\) - 2 \(\ge\) 0

\(\sqrt{x-4}\) \(\ge\) 2

x - 4 \(\ge\) 4

x \(\ge\) 8

=> \(\sqrt{x-4}\) + 2 + \(\sqrt{x-4}\) - 2 = 4

<=> x=8 (TM)

+ TH2: \(\sqrt{x-4}\) - 2 < 0

\(\sqrt{x-4}\) < 2

x-4 < 4

x < 8

kết hợp vs dk thì x = 8

Vậy x = 8