Question

Rút gọn biểu thức 

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

Answer 1

Ta có: \(\dfrac{3\left(\sqrt{5}-1\right)}{\left(\sqrt{5}+1\right)\left(\sqrt{5}+1\right)}\)

\(=\dfrac{3\left(\sqrt{5}-1\right)}{6+2\sqrt{5}}\)

\(=\dfrac{3\left(\sqrt{5}-1\right)\left(6-2\sqrt{5}\right)}{\left(6-2\sqrt{5}\right)\left(6+2\sqrt{5}\right)}\)

\(=\dfrac{3\left(6\sqrt{5}-10-6+2\sqrt{5}\right)}{16}\)

\(=\dfrac{3\left(8\sqrt{5}-16\right)}{16}\)

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