giúp mik vs giải phương trình $\sqrt{\sqrt{5} +\sqrt{5+32\sqrt{69-16\sqrt{5}} }}$

Question

giúp mik vs
giải phương trình
$\sqrt{\sqrt{5} +\sqrt{5+32\sqrt{69-16\sqrt{5}} }}$

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Jasmine 1 năm 2021-09-09T18:41:56+00:00 2 Answers 13 views 0

Answers ( )

  1. aikhanh
    0
    2021-09-09T18:43:05+00:00
    Reply

    $\sqrt{\sqrt{5}+\sqrt{5+32\sqrt{69-16\sqrt{5}}}}$

    $= \sqrt{\sqrt{5}+\sqrt{5+32\sqrt{69-2.8.\sqrt{5}}}}$

    $= \sqrt{\sqrt{5}+\sqrt{5+32\sqrt{(8-\sqrt{5})^2}}}$

    $= \sqrt{\sqrt{5}+\sqrt{5+32(8-\sqrt{5)}}}$

    $= \sqrt{\sqrt{5}+\sqrt{5+256-32\sqrt{5}}}$

    $= \sqrt{\sqrt{5}+\sqrt{256-2.16\sqrt{5}+5}}$

    $= \sqrt{\sqrt{5}+\sqrt{(16-\sqrt{5})^2}}$

    $= \sqrt{\sqrt{5}+16-\sqrt{5}}$

    $= \sqrt{16}$

    $= 4$

  3. danthu
    0
    2021-09-09T18:43:38+00:00
    Reply

    CHÚC BẠN HỌC TỐT !!!!!!!!

    Đáp án:

      $= 4$

    Giải thích các bước giải:

        $\sqrt{\sqrt{5} + \sqrt{5 + 32\sqrt{69 – 16\sqrt{5}}}}$

    $= \sqrt{\sqrt{5} + \sqrt{5 + 32\sqrt{64 – 16\sqrt{5} + 5}}}$

    $= \sqrt{\sqrt{5} + \sqrt{5 + 32\sqrt{(8 – \sqrt{5})²}}}$

    $= \sqrt{\sqrt{5} + \sqrt{5 + 32|8 – \sqrt{5}|}}$

    $= \sqrt{\sqrt{5} + \sqrt{5 + 32(8 – \sqrt{5})}}$

    $= \sqrt{\sqrt{5} + \sqrt{5 + 256 – 32\sqrt{5}}}$

    $= \sqrt{\sqrt{5} + \sqrt{256 – 32\sqrt{5} + 5}}$

    $= \sqrt{\sqrt{5} + \sqrt{(16 – \sqrt{5})²}}$

    $= \sqrt{\sqrt{5} + |16 – \sqrt{5}|}$

    $= \sqrt{\sqrt{5} + 16 – \sqrt{5}}$

    $= \sqrt{16}$

    $= 4$

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