Question

Rút gọn \(\left(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\right)^2\)

Answer 1

\(\left(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\right)^2\)

=\(\left(\sqrt{3-\sqrt{5}}\right)^2+2\sqrt{3-\sqrt{5}}.\sqrt{3+\sqrt{5}}+\left(\sqrt{3+\sqrt{5}}\right)^2\)

=\(3-\sqrt{5}+2\sqrt{\left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right)}+3+\sqrt{5}\)

=\(6+2\sqrt{9-\left(\sqrt{5}\right)^2}=6+2\sqrt{9-5}=6+2\sqrt{4}\)

=\(6+2.2=6+4=10\)

Answer 2

Để giải xem thử:       

      \(\left(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\right)^2\)        

\(=\left(\sqrt{3.1-\sqrt{5.1}}+\sqrt{3.1+\sqrt{5.1}}\right)^2\)        

\(=\left(\sqrt{3.1-\sqrt{5.1}}+\sqrt{3.1+\sqrt{5.1}}\right).\left(\sqrt{3.1-\sqrt{5.1}}+\sqrt{3.1+\sqrt{5.1}}\right)=10\)