Question

[duc99duc]

\(\sqrt{3+\sqrt{5}}+\sqrt{3-\sqrt{5}}\)   hộ anh em ơi mai nộp rồi

Answer 1

[Đỗ Quỳnh Anh]

Đặt bth đã cho là A, ta có:

A²=3−√5+3+√5+2√3−√5.√3+√53−5+3+5+23−5.3+5

A²=6+2√(3−√5)(3+√5)6+2(3−5)(3+5)

A^{2=6+2√9−56+29−5}

A²=6+4=10

 ( Tôi giúp ng ae rồi đấy, ok thì kb nhoa) =33

A=√10

Answer 2

[Chu Phúc Hưng]

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

=\(\frac{\sqrt{6+2\sqrt{5}}}{\sqrt{2}}+\frac{\sqrt{6-2\sqrt{5}}}{\sqrt{2}}\)

=\(\frac{\sqrt{\left(\sqrt{5}+1\right)^2}}{\sqrt{2}}+\frac{\sqrt{\left(\sqrt{5}-1\right)^2}}{\sqrt{2}}\)

=\(\frac{\sqrt{5}+1+\sqrt{5}-1}{\sqrt{2}}\)

=\(\frac{2\sqrt{5}}{\sqrt{2}}\)

=\(\sqrt{2}\sqrt{5}\)=\(\sqrt{10}\)