Question

вычислите √(12-√13)² + √(3-√13)²

Answer 1

$\sqrt{ {(12 - \sqrt{13} )}^{2} } + \sqrt{ {(3 - \sqrt{13} )}^{2} } = \\ 12 - \sqrt{13 } + \sqrt{13} - 3 = 9$

Answer 2

$\boxed {\sqrt{a^2}=|a|=\left \{ {{a\; ,\; esli\; a\geq 0\; ,} \atop {-a\; ,\; esli\; a<0\; .}} \right. }\\\\\\\sqrt{12-\sqrt{13}}+\sqrt{3-\sqrt{13}}=|12-\sqrt{13}|+|3-\sqrt{13}|=\\\\\\\star \; \; 3<\sqrt{13}<4,\; t.k.\; 13>3^2=9\; \; ,\; 13<4^2=16\; \; \Rightarrow \\\\(12-\sqrt{13})>0\; \; i\; \; |12-\sqrt{13}|=12-\sqrt{13}\; ;\\\\(3-\sqrt{13})<0\; \; \Rightarrow \; \; |3-\sqrt{13}|=-(3-\sqrt{13})=\sqrt{13}-3\; \; \star \\\\\\=12-\sqrt{13}+\sqrt{13}-3=12-3=9$