Cho a va b la cac so duong thoa man : a^218+b^2018 = a^2019+b^2019 = a^2020 +b^2020. . Tinh K = a^2021+ b^2021

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1. Đáp án:

   \[K = 2\]

   Giải thích các bước giải:

    Ta có:

   \(\begin{array}{l}
   {a^{2018}} + {b^{2018}} = {a^{2019}} + {b^{2019}}\\
    \Leftrightarrow {a^{2018}} – {a^{2018}} = {b^{2019}} – {b^{2018}}\\
    \Leftrightarrow {a^{2018}}\left( {1 – a} \right) = {b^{2018}}\left( {b – 1} \right)\\
    \Leftrightarrow \frac{{1 – a}}{{b – 1}} = \frac{{{b^{2018}}}}{{{a^{2018}}}}\\
   {a^{2019}} + {b^{2019}} = {a^{2020}} + {b^{2020}}\\
    \Leftrightarrow {a^{2019}} – {a^{2020}} = {b^{2020}} – {b^{2019}}\\
    \Leftrightarrow {a^{2019}}\left( {1 – a} \right) = {b^{2019}}\left( {b – 1} \right)\\
    \Leftrightarrow \frac{{1 – a}}{{b – 1}} = \frac{{{b^{2019}}}}{{{a^{2019}}}}\\
    \Rightarrow \frac{{{b^{2018}}}}{{{a^{2018}}}} = \frac{{{b^{2019}}}}{{{a^{2019}}}} \Leftrightarrow \frac{b}{a} = 1 \Leftrightarrow a = b\\
    \Rightarrow 2{a^{2018}} = 2{a^{2019}} \Rightarrow a = b = 1\\
    \Rightarrow K = {a^{2021}} + {b^{2021}} = 1 + 1 = 2
   \end{array}\)

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