Вычислите : (√(7+√13) - √(7-√13))²

[latex]( \sqrt{7+ \sqrt{13} } - \sqrt{7- \sqrt{13} })^2= \\ =( \sqrt{7+ \sqrt{13} })^2 - 2\sqrt{7+ \sqrt{13}}\sqrt{7- \sqrt{13}}+(\sqrt{7- \sqrt{13} })^2= \\ =7+ \sqrt{13} -2 \sqrt{(7+ \sqrt{13})(7- \sqrt{13})} +7- \sqrt{13} = \\ =14-2 \sqrt{7^2-( \sqrt{13})^2 } =14-2 \sqrt{49-13}=14-2 \sqrt{36} = \\ =14-2 \sqrt{6^2}=14-2*6=14-12=2 [/latex]