Question

So sánh A và B

Answer 1

\(A=\sqrt{6+\sqrt{6+\sqrt{6}}}+\sqrt{2+\sqrt{2+\sqrt{2}}}< \sqrt{6+\sqrt{6+\sqrt{9}}}+\sqrt{2+\sqrt{2+\sqrt{4}}}=\sqrt{6+\sqrt{6+3}}+\sqrt{2+\sqrt{2+2}}=\sqrt{6+\sqrt{9}}+\sqrt{2+\sqrt{4}}=\sqrt{6+3}+\sqrt{2+2}=\sqrt{9}+\sqrt{4}=3+2=5\)

Answer 2

\(\sqrt{6+\sqrt{6+\sqrt{6}}}+\sqrt{2+\sqrt{2+\sqrt{2}}}< \sqrt{6+\sqrt{6+\sqrt{9}}}+\sqrt{2+\sqrt{2+\sqrt{4}}}=5\)

\(\Rightarrow A< B\)