Используя бином Ньютона, найдите разложение: ([tex] \sqrt{5} [/tex] + 2[tex] \sqrt{3} [/tex])^4. Created by walt55. matematika-ru

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walt55 @walt55

July 2022 1 7 Report

Используя бином Ньютона, найдите разложение:
([tex] \sqrt{5} [/tex] + 2[tex] \sqrt{3} [/tex])^4

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NNNLLL54

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$(\sqrt5+2\sqrt3)^4=(\sqrt5)^4+4\cdot (\sqrt5)^3\cdot 2\sqrt3+6\cdot (\sqrt5)^2\cdot (2\sqrt3)^2+\\\\+4\cdot \sqrt5\cdot (2\sqrt3)^3+(2\sqrt3)^4=\\\\=25+40\sqrt{15}+360+96\sqrt{15}+144=529+136\sqrt{15}$

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