[tex] \frac{1- \sqrt{21} }{ \sqrt{3}+ \sqrt{7} } + \frac{26}{3 \sqrt{3}-1 }- \sqrt{21}-(

Ответы 1

$\frac{1-\sqrt{21}}{\sqrt{3}+\sqrt{7}}+\frac{26}{3\sqrt{3}-1}-\sqrt{21}-(\sqrt{7}-1)(1-\sqrt{3})= \\ \\ =\frac{1-\sqrt{21}}{\sqrt{3}+\sqrt{7}}+\frac{26}{3\sqrt{3}-1}-\sqrt{21}-(\sqrt{7}-\sqrt{21}-1+\sqrt{3})= \\ \\ =\frac{1-\sqrt{21}}{\sqrt{3}+\sqrt{7}}+\frac{26}{3\sqrt{3}-1}-\sqrt{21}-\sqrt{7}+\sqrt{21}+1-\sqrt{3}= \\ \\ =\frac{1-\sqrt{21}}{\sqrt{3}+\sqrt{7}}+\frac{26}{3\sqrt{3}-1}-\sqrt{7}+1-\sqrt{3}= \\ \\ =\frac{1-\sqrt{21}}{\sqrt{3}+\sqrt{7}}+\frac{26}{3\sqrt{3}-1}-(\sqrt{7}-1+\sqrt{3})=$ $=\frac{(1-\sqrt{21})(3\sqrt{3}-1)+26(\sqrt{3}+\sqrt{7})-(-1+\sqrt{3}+\sqrt{7})(\sqrt{3}+\sqrt{7})(3\sqrt{3}-1)}{(\sqrt{3}+\sqrt{7})(3\sqrt{3}-1)}=$ $=\frac{(-1+3\sqrt{3}-9\sqrt{7}+\sqrt{21})+(26\sqrt{3}+26\sqrt{7})-(-1+\sqrt{3}+\sqrt{7})(9-\sqrt{3}-\sqrt{7}+3\sqrt{21})}{9-\sqrt{3}-\sqrt{7}+3\sqrt{21}}= \\ \\ =\frac{(-1+3\sqrt{3}-9\sqrt{7}+\sqrt{21})+(26\sqrt{3}+26\sqrt{7})-(-19+31\sqrt{3}+19\sqrt{7}-5\sqrt{21})}{9-\sqrt{3}-\sqrt{7}+3\sqrt{21}}= \\ \\ =\frac{-1+3\sqrt{3}-9\sqrt{7}+\sqrt{21}+26\sqrt{3}+26\sqrt{7}+19-31\sqrt{3}-19\sqrt{7}+5\sqrt{21}}{9-\sqrt{3}-\sqrt{7}+3\sqrt{21}}=$ $=\frac{18-2\sqrt{3}-2\sqrt{7}+6\sqrt{21}}{9-\sqrt{3}-\sqrt{7}+3\sqrt{21}} =\frac{2(9-\sqrt{3}-\sqrt{7}+3\sqrt{21})}{9-\sqrt{3}-\sqrt{7}+3\sqrt{21}}=2$
- Автор:
  monteen4yjn
- 5 лет назад
- 0
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