Ответ:
[tex]a)\ \sqrt3+1\\\\b)\ 9\sqrt5-19\\\\g)\ \sqrt{10}-1[/tex]
Объяснение:
[tex]a)\\\\(\sqrt3-1)(\sqrt3+2)=\sqrt3\cdot\sqrt3-\sqrt3 \cdot 2-\sqrt1\cdot \sqrt3+1\cdot 2=\\\\3+2\sqrt3-\sqrt3-2=\sqrt3+1\\\\b)\\\\(2\sqrt5-3)(3-\sqrt5)=2\sqrt5\cdot 3-2\sqrt 5\cdot \sqrt5-3\cdot 3+3\cdot\sqrt5=\\\\6\sqrt5-10-9+3\sqrt5=9\sqrt5-19\\\\g)\\\\(2\sqrt2-\sqrt5)(\sqrt2+\sqrt5)=2\sqrt2\cdot \sqrt2+2\sqrt2 \cdot \sqrt5-\sqrt5\cdot \sqrt2-\sqrt5 \cdot \sqrt5=\\\\4+2\sqrt{10}-\sqrt{10}-5=\sqrt{10}-1[/tex]
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Answers & Comments
Ответ:
[tex]a)\ \sqrt3+1\\\\b)\ 9\sqrt5-19\\\\g)\ \sqrt{10}-1[/tex]
Объяснение:
[tex]a)\\\\(\sqrt3-1)(\sqrt3+2)=\sqrt3\cdot\sqrt3-\sqrt3 \cdot 2-\sqrt1\cdot \sqrt3+1\cdot 2=\\\\3+2\sqrt3-\sqrt3-2=\sqrt3+1\\\\b)\\\\(2\sqrt5-3)(3-\sqrt5)=2\sqrt5\cdot 3-2\sqrt 5\cdot \sqrt5-3\cdot 3+3\cdot\sqrt5=\\\\6\sqrt5-10-9+3\sqrt5=9\sqrt5-19\\\\g)\\\\(2\sqrt2-\sqrt5)(\sqrt2+\sqrt5)=2\sqrt2\cdot \sqrt2+2\sqrt2 \cdot \sqrt5-\sqrt5\cdot \sqrt2-\sqrt5 \cdot \sqrt5=\\\\4+2\sqrt{10}-\sqrt{10}-5=\sqrt{10}-1[/tex]