Mình xin phép làm câu đầu nhé:
$\sqrt[]{x+2\sqrt[]{x-1}}$-$\sqrt[]{x-2\sqrt[]{x-1}}$≤2
⇒$\sqrt[]{x-1+2\sqrt[]{x-1}+1}$-$\sqrt[]{x-1-2\sqrt[]{x-1}+1}$≤2
⇒$\sqrt[]{(\sqrt[]{x-1})^{2}+2\sqrt[]{x-1}.1+1^{2}}$-$\sqrt[]{(\sqrt[]{x-1})^{2}-2\sqrt[]{x-1}.1+1^{2}}$≤2
⇒$\sqrt[]{(\sqrt[]{x-1}+1)^{2}}$-$\sqrt[]{(\sqrt[]{x-1}-1)^{2}}$≤2
⇒|$\sqrt[]{x-1}$+1|-|$\sqrt[]{x-1}$-1|≤2
⇒$\sqrt[]{x-1}$+1-($\sqrt[]{x-1}$-1)≤2 (vì x≥1)
⇒$\sqrt[]{x-1}$+1-$\sqrt[]{x-1}$+1≤2
⇒2≤2 (đúng)
⇒điều phải chứng minh
