Question

\(\text{So sánh 2 số }:A=\sqrt{4+\sqrt{7}}\text{ và }B=\sqrt{4-\sqrt{7}}+\sqrt{2}\)

Answer 1

\(\sqrt{2}B=\sqrt{8-2\sqrt{7}}+2=\sqrt{\left(\sqrt{7}-1\right)^2}+2=\sqrt{7}-1+2=\sqrt{7}+1\)

\(\sqrt{2}A=\sqrt{8+2\sqrt{7}}=\sqrt{\left(\sqrt{7}+1\right)^2}=\sqrt{7}+1\)

Vậy A = B 

Answer 2

A = 11 

B = 7 

--> A > B 

Answer 3

\(A\sqrt{2}=\sqrt{8+2\sqrt{7}}=\sqrt{\left(\sqrt{7}\right)^2+2\sqrt{7}+1}=\sqrt{\left(\sqrt{7}+1\right)^2}=\sqrt{7}+1\)

\(B\sqrt{2}=\sqrt{8-2\sqrt{7}}+\left(\sqrt{2}\right)^2=\sqrt{\left(\sqrt{7}-1\right)^2}+2=\sqrt{7}-1+2=\sqrt{7}+1\)

=> \(A\sqrt{2}=B\sqrt{2}\) => A = B