cho $\frac{a}{b}$ = $\frac{b}{3c}$ = $\frac{c}{3a}$ chứng minh: b= c

Question

cho $\frac{a}{b}$ = $\frac{b}{3c}$ = $\frac{c}{3a}$ chứng minh: b= c

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Eliza 2 tuần 2021-07-12T10:58:01+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-07-12T10:59:33+00:00

    Giải thích các bước giải:

    Ta có:

    \(\begin{array}{l}
    \dfrac{a}{b} = \dfrac{b}{{3c}} = \dfrac{c}{{3a}}\\
     \Rightarrow \left\{ \begin{array}{l}
    \dfrac{a}{b} = \dfrac{b}{{3c}}\\
    \dfrac{b}{{3c}} = \dfrac{c}{{3a}}
    \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
    3ac = {b^2}\\
    3ab = 3{c^2}
    \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
    a = \dfrac{{{b^2}}}{{3c}}\\
    a = \dfrac{{{c^2}}}{b}
    \end{array} \right. \Rightarrow \dfrac{{{b^2}}}{{3c}} = \dfrac{{{c^2}}}{b} \Leftrightarrow {b^3} = 3{c^3} \Rightarrow b = \sqrt[3]{3}.c
    \end{array}\)

    Em xem lại đề câu này nhé!

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