Задание 9. Найдите значение выражения: 1 (17-3)(17+3); 2 (√23-2)(√23+2); 3 (√47-5)(√47+5); 4 (√29-4)(√29+4); 5 (√41-3)(√41+3); 6 (13-2)(13+2); 7 (√7-√3)(√7+√3); 8 (13-√2)(13+√2); 9 (17-√5)(17+√5); 10 (19-√2)(19+√2); 11 (√5-√3)(√5+√3); 12 (√7-√5)(√7+√5); 13 (19-7)2+14/19; 14 (13-3)2+6/13; 15 (11-7)2+14/11; 16 (√5+9)2-18√5; 17 (17+2)²-4/17; 18 (√3+8)2-16√3.

Задание 9. Найдите значение выражения:

1. $$(17 - 3)(17 + 3) = 17^2 - 3^2 = 289 - 9 = 280$$.

2. $$(\sqrt{23} - 2)(\sqrt{23} + 2) = (\sqrt{23})^2 - 2^2 = 23 - 4 = 19$$.

3. $$(\sqrt{47} - 5)(\sqrt{47} + 5) = (\sqrt{47})^2 - 5^2 = 47 - 25 = 22$$.

4. $$(\sqrt{29} - 4)(\sqrt{29} + 4) = (\sqrt{29})^2 - 4^2 = 29 - 16 = 13$$.

5. $$(\sqrt{41} - 3)(\sqrt{41} + 3) = (\sqrt{41})^2 - 3^2 = 41 - 9 = 32$$.

6. $$(13 - 2)(13 + 2) = 13^2 - 2^2 = 169 - 4 = 165$$.

7. $$(\sqrt{7} - \sqrt{3})(\sqrt{7} + \sqrt{3}) = (\sqrt{7})^2 - (\sqrt{3})^2 = 7 - 3 = 4$$.

8. $$(13 - \sqrt{2})(13 + \sqrt{2}) = 13^2 - (\sqrt{2})^2 = 169 - 2 = 167$$.

9. $$(17 - \sqrt{5})(17 + \sqrt{5}) = 17^2 - (\sqrt{5})^2 = 289 - 5 = 284$$.

10. $$(19 - \sqrt{2})(19 + \sqrt{2}) = 19^2 - (\sqrt{2})^2 = 361 - 2 = 359$$.

11. $$(\sqrt{5} - \sqrt{3})(\sqrt{5} + \sqrt{3}) = (\sqrt{5})^2 - (\sqrt{3})^2 = 5 - 3 = 2$$.

12. $$(\sqrt{7} - \sqrt{5})(\sqrt{7} + \sqrt{5}) = (\sqrt{7})^2 - (\sqrt{5})^2 = 7 - 5 = 2$$.

13. $$(19-7)^2 + \frac{14}{19} = 12^2 + \frac{14}{19} = 144 + \frac{14}{19} = \frac{144 \cdot 19 + 14}{19} = \frac{2736 + 14}{19} = \frac{2750}{19} \approx 144.74$$.

14. $$(13-3)^2 + \frac{6}{\sqrt{13}} = 10^2 + \frac{6}{\sqrt{13}} = 100 + \frac{6}{\sqrt{13}} \approx 101.66$$.

15. $$(11-7)^2 + \frac{14}{\sqrt{11}} = 4^2 + \frac{14}{\sqrt{11}} = 16 + \frac{14}{\sqrt{11}} \approx 20.22$$.

16. $$(\sqrt{5}+9)^2 - 18\sqrt{5} = (\sqrt{5})^2 + 2 \cdot \sqrt{5} \cdot 9 + 9^2 - 18\sqrt{5} = 5 + 18\sqrt{5} + 81 - 18\sqrt{5} = 86$$.

17. $$(\sqrt{17}+2)^2 - 4\sqrt{17} = (\sqrt{17})^2 + 2 \cdot \sqrt{17} \cdot 2 + 2^2 - 4\sqrt{17} = 17 + 4\sqrt{17} + 4 - 4\sqrt{17} = 21$$.

18. $$(\sqrt{3}+8)^2 - 16\sqrt{3} = (\sqrt{3})^2 + 2 \cdot \sqrt{3} \cdot 8 + 8^2 - 16\sqrt{3} = 3 + 16\sqrt{3} + 64 - 16\sqrt{3} = 67$$.

Ответ: 1) 280; 2) 19; 3) 22; 4) 13; 5) 32; 6) 165; 7) 4; 8) 167; 9) 284; 10) 359; 11) 2; 12) 2; 13) $$ \frac{2750}{19} $$; 14) $$100 + \frac{6}{\sqrt{13}}$$; 15) $$16 + \frac{14}{\sqrt{11}}$$; 16) 86; 17) 21; 18) 67