Question

Trục căn thức ở mẫu: \(\dfrac{1+\sqrt{5}}{\sqrt{15}-\sqrt{5}+\sqrt{3}-1}\)

Answer 1

Theo mình thì làm như vầy nha:

\(\dfrac{1+\sqrt{5}}{\sqrt{15}-\sqrt{5}+\sqrt{3}-1}\)

=\(\dfrac{1+\sqrt{5}}{\left(\sqrt{15}-\sqrt{5}\right)+\left(\sqrt{3}-1\right)}\)

=\(\dfrac{1+\sqrt{5}}{\sqrt{5}\left(\sqrt{3}-1\right)+\left(\sqrt{3}-1\right)}\)

=\(\dfrac{1+\sqrt{5}}{\left(1+\sqrt{5}\right)\left(\sqrt{3}-1\right)}\)

=\(\dfrac{1}{\sqrt{3}-1}\)

=\(\dfrac{\sqrt{3}+1}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}\)

=\(\dfrac{\sqrt{3}+1}{3-1}\)

=\(\dfrac{\sqrt{3}+1}{2}\)