1. Упростите выражения: а) \(\frac{1}{2}\sqrt{200} - 7\sqrt{\frac{2}{49}} - \sqrt{72}\) б) \((2\sqrt{5}+1)(\sqrt{20}-2)\) в) \((\sqrt{3}-1)^2 - (2+\sqrt{3})^2\)

1. Упростите выражения:

1. а)

   \(\frac{1}{2}\sqrt{200} - 7\sqrt{\frac{2}{49}} - \sqrt{72}\) = \(\frac{1}{2} \cdot 10\sqrt{2} - 7 \cdot \frac{\sqrt{2}}{7} - 6\sqrt{2}\) = \(5\sqrt{2} - \sqrt{2} - 6\sqrt{2}\) = \(-2\sqrt{2}\)

2. б)

   \((2\sqrt{5}+1)(\sqrt{20}-2)\) = \((2\sqrt{5}+1)(2\sqrt{5}-2)\) = \((2\sqrt{5})^2 - 2\sqrt{5} \cdot 2 + 1 \cdot 2\sqrt{5} - 2\) = \(20 - 4\sqrt{5} + 2\sqrt{5} - 2\) = \(18 - 2\sqrt{5}\)

3. в)

   \((\sqrt{3}-1)^2 - (2+\sqrt{3})^2\) = \((3 - 2\sqrt{3} + 1) - (4 + 4\sqrt{3} + 3)\) = \((4 - 2\sqrt{3}) - (7 + 4\sqrt{3})\) = \(4 - 2\sqrt{3} - 7 - 4\sqrt{3}\) = \(-3 - 6\sqrt{3}\)

Ответ: а) -2√2; б) 18 - 2√5; в) -3 - 6√3.