Theo bài toán:
\(a+b=7\Rightarrow\left(a+b\right)^2=49\)
\(\Leftrightarrow a^2+2ab+b^2=49\)
\(\Leftrightarrow a^2+b^2=49-2ab=49-2.12=25\)
\(\Rightarrow a^2-2ab+b^2=\left(a+b\right)^2\)
\(\Leftrightarrow\left(a^2+b^2\right)-2ab=\left(a+b\right)^2\)
\(\Leftrightarrow25-2.12=\left(a+b\right)^2\)
\(\Leftrightarrow\left(a+b\right)^2=1\Rightarrow\left[{}\begin{matrix}a+b=1\\a+b=-1\end{matrix}\right.\)
Vậy : \(\left[{}\begin{matrix}\left(a+b\right)^{2017}=1^{2017}=1\\\left(a+b\right)^{2017}=-1^{2017}=-1\end{matrix}\right.\)
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