$\sqrt{x+2\sqrt{x-1} }=2$

Đáp án:

 Điều kiện: x≥1

$\sqrt[]{x+2\sqrt[]{x-1}}$ = 2

⇔  $\sqrt[]{x-1+2\sqrt[]{x-1}+1}$ = 2

⇔  $\sqrt[]{(\sqrt[]{x-1} +1}$)² = 2

⇔ | $\sqrt[]{x-1}$ +1 | = 2

⇔  $\sqrt[]{x-1}$ +1 = 2

⇔  $\sqrt[]{x-1}$ = 1

⇔ x - 1 = 1

⇔ x = 2 (TMĐK)