이중근호 유리화 계산

$x$$\displaystyle = \frac{1 + \sqrt{2} + \sqrt{3}}{1 - \sqrt{2} + \sqrt{3}}$ $\displaystyle = \frac{( 1 + \sqrt{2} + \sqrt{3} ) ^{2}}{( 1 - \sqrt{2} + \sqrt{3} ) ( 1 + \sqrt{2} + \sqrt{3} )}$ $\displaystyle = \frac{3 + \sqrt{2} + \sqrt{3} + \sqrt{6}}{1 + \sqrt{3}}$ $\displaystyle = \frac{\sqrt{3} ( 1 + \sqrt{3} ) + \sqrt{2} ( 1 + \sqrt{3} )}{1 + \sqrt{3}}$ $\displaystyle = \sqrt{3} + \sqrt{2}$ $\displaystyle \therefore x ( x - \sqrt{2} ) ( x - \sqrt{3} ) = ( \sqrt{3} - \sqrt{2} ) \sqrt{3} \sqrt{2}$ $\displaystyle = 3 \sqrt{2} + 2 \sqrt{3}$