Question

Tìm số nguyên tố P ; Q ; R thỏa mãn: P² + Q² + R² = 6P + 4Q + 2R

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Answer 1

\(\Leftrightarrow p^2-6p+9+q^2-4q+4+r^2-2r+1=14\)

\(\Leftrightarrow\left(p-3\right)^2+\left(q-2\right)^2+\left(r-1\right)^2=14=1+4+9\)

\(\left\{{}\begin{matrix}\left(p-3\right)^2=4\\\left(q-2\right)^2=9\\\left(r-1\right)^2=1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}p=5\\q=5\\r=2\end{matrix}\right.\)