Question

Chứng minh:

a. 9+4\(\sqrt{5}\)= (\(\sqrt{5}\)+2)²

b. \(\sqrt{23+8\sqrt{ }7}\) - \(\sqrt{7}\) = 4

Answer 1

a. 9+4\(\sqrt{5}\)=(\(\sqrt{5}\)​+2)2

VT: 9+4\(\sqrt{5}\)=2\(^2\)+2.2.​\(\sqrt{5}\)​+​​(\(\sqrt{5}\))\(^2\)=(2+\(\sqrt{5}\))\(^2\)=VP

b. \(\sqrt{23+8\sqrt{7}}\)-\(\sqrt{7}\)=4

\(\Leftrightarrow\)\(\sqrt{4^2+2.4\sqrt{7}+\left(\sqrt{7}\right)^2}\)-\(\sqrt{7}\)=4

\(\Leftrightarrow\)\(\sqrt{4+\sqrt{7}}^2\)-\(\sqrt{7}\)=4

\(\Leftrightarrow\)4+\(\sqrt{7}\)-\(\sqrt{7}\)=4

\(\Leftrightarrow\)4=4

\(\Rightarrow\)VT=VP
\(\sqrt{5}\)\(\sqrt{5}\)