tex]...

July 2021 1 9 Report

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1)
[tex] (\sqrt{21} + \sqrt{14} - 2 \sqrt{35} ) \times \frac{ \sqrt{7} }{7} + \sqrt{20} [/tex]
2)
[tex]( \sqrt{5} + \sqrt{3} - \sqrt{15} )( \sqrt{5} - \sqrt{3} ) + \sqrt{75} [/tex]

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$1)\; \; (\sqrt{21}+\sqrt{14}-2\sqrt{35})\cdot \frac{\sqrt7}{7}+\sqrt{20}=\\\\=(\sqrt{7\cdot 3}+\sqrt{7\cdot 2}-2\sqrt{7\cdot 5})\cdot \frac{\sqrt7}{7}+\sqrt{20}=\frac{7\sqrt{3}+7\sqrt2-2\cdot 7\sqrt5}{7}+\sqrt{4\cdot 5}=\\\\=\sqrt3+\sqrt2-2\sqrt5+2\sqrt5=\sqrt3+\sqrt2$

$2)\; \; (\sqrt5+\sqrt3-\sqrt{15})(\sqrt5-\sqrt3)+\sqrt{75}=\\\\=(\sqrt5-\sqrt3)(\sqrt5+\sqrt3)-\sqrt{75}+\sqrt{45}+\sqrt{75}=\\\\=5-3+\sqrt{9\cdot 5}=2+3\sqrt5$

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