![1)\; \; (2+\sqrt{17})(2-\sqrt{17})=4-17=-13\\\\2)\; \; \sqrt5\cdot (\sqrt{45}+3)-(\sqrt{45}+2)=\sqrt{5\cdot 45}+3\sqrt5-\sqrt{45}-2=\\\\=\sqrt{5^2\cdot 9}+3\sqrt5-\sqrt{9\cdot 5}-2=5\cdot 3+3\sqrt5-3\sqrt5-2=13 1)\; \; (2+\sqrt{17})(2-\sqrt{17})=4-17=-13\\\\2)\; \; \sqrt5\cdot (\sqrt{45}+3)-(\sqrt{45}+2)=\sqrt{5\cdot 45}+3\sqrt5-\sqrt{45}-2=\\\\=\sqrt{5^2\cdot 9}+3\sqrt5-\sqrt{9\cdot 5}-2=5\cdot 3+3\sqrt5-3\sqrt5-2=13](https://tex.z-dn.net/?f=1%29%5C%3B%20%5C%3B%20%282%2B%5Csqrt%7B17%7D%29%282-%5Csqrt%7B17%7D%29%3D4-17%3D-13%5C%5C%5C%5C2%29%5C%3B%20%5C%3B%20%5Csqrt5%5Ccdot%20%28%5Csqrt%7B45%7D%2B3%29-%28%5Csqrt%7B45%7D%2B2%29%3D%5Csqrt%7B5%5Ccdot%2045%7D%2B3%5Csqrt5-%5Csqrt%7B45%7D-2%3D%5C%5C%5C%5C%3D%5Csqrt%7B5%5E2%5Ccdot%209%7D%2B3%5Csqrt5-%5Csqrt%7B9%5Ccdot%205%7D-2%3D5%5Ccdot%203%2B3%5Csqrt5-3%5Csqrt5-2%3D13)
6,25\; \; \Rightarrow \; \; \sqrt{8+2\sqrt{15}}>\sqrt{13-2\sqrt{30}}" alt="3)\; \; \sqrt{8+2\sqrt{15}}\; \; \vee \; \; \sqrt{13-2\sqrt{30}}\\\\ 8+2\sqrt{15}\; \; \vee\; \; 13-2\sqrt{30}\\\\2\sqrt{15}+2\sqrt{30} \; \; \vee\; \; 5\\\\2(\sqrt{15}+\sqrt{30})\; \; \vee \; \; 5\\\\15+30+2\sqrt{15\cdot 30}\; \; \vee \; \; (\frac{5}{2})^2\\ \\ 45+2\cdot 15\sqrt2\; \; \vee \; \; 6,25\\ \\45+30\sqrt2>6,25\; \; \Rightarrow \; \; \sqrt{8+2\sqrt{15}}>\sqrt{13-2\sqrt{30}}" align="absmiddle" class="latex-formula">