giupms mik với mn ơi

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giupms mik với mn ơi
giupms-mik-voi-mn-oi

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Acacia 1 year 2020-11-10T05:59:54+00:00 1 Answers 57 views 0

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    2020-11-10T06:01:10+00:00

    Đáp án:

     

    Giải thích các bước giải:

    Ta có:

    $2(\sqrt[3]{8+3\sqrt{21}}+\sqrt[3]{8-3\sqrt{21}})$

    $=2\sqrt[3]{8+3\sqrt{21}}+2\sqrt[3]{8-3\sqrt{21}})$

    $=\sqrt[3]{64+24\sqrt{21}}+\sqrt[3]{64-24\sqrt{21}}$

    $=\sqrt[3]{1+3\sqrt{21}+63+21\sqrt{21}}+\sqrt[3]{1-3\sqrt{21}+63-21\sqrt{21}}$

    $=\sqrt[3]{1^3+3.1^2.\sqrt{21}+3.1.(\sqrt{21})^2+(\sqrt{21})^3}+\sqrt[3]{1^3-3.1^2.\sqrt{21}+3.1.(\sqrt{21})^2-(\sqrt{21})^3}$

    $=\sqrt[3]{(1+\sqrt{21})^3}+\sqrt[3]{(1-\sqrt{21})^3}$

    $=1+\sqrt{21}+1\sqrt{21}$

    $=2$

    $⇒\sqrt[3]{8+3\sqrt{21}}+\sqrt[3]{8-3\sqrt{21}}=1$ (đpcm)

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