Giải thích các bước giải:
Ta có :
$x\sqrt{5}-(1+\sqrt{3})y=1$
$\to (1+\sqrt{3})y=x\sqrt{5}-1$
$\to y=\dfrac{x\sqrt{5}-1}{1+\sqrt{3}}$
$\to (1-\sqrt{3})x+\dfrac{x\sqrt{5}-1}{1+\sqrt{3}}.\sqrt{5}=1$
$\to (1-\sqrt{3})x+\dfrac{x\sqrt{5}-1}{1+\sqrt{3}}.\sqrt{5}=1$
$\to \left(1-\sqrt{3}\right)x\left(1+\sqrt{3}\right)+\frac{\sqrt{5}\left(\sqrt{5}x-1\right)}{1+\sqrt{3}}\left(1+\sqrt{3}\right)=1\cdot \left(1+\sqrt{3}\right)$
$\to \left(1-\sqrt{3}\right)\left(1+\sqrt{3}\right)x+\sqrt{5}\left(\sqrt{5}x-1\right)=1+\sqrt{3}$
$\to -2x+5x-\sqrt{5}=1+\sqrt{3}$
$\to 3x-\sqrt{5}=1+\sqrt{3}$
$\to x=\dfrac{1+\sqrt{3}+\sqrt{5}}{3}$
$\to y=\dfrac{x\sqrt{5}-1}{1+\sqrt{3}}=\dfrac{\sqrt{3}+\sqrt{5}-1}{3}$
