Question

GPT nghiệm nguyên:

\(x^2+y^2-2x+y=9\)

Answer 1

\(x^2+y^2-2x+y=9\)

\(\Rightarrow-2x^3-y^2=9\)

\(\Rightarrow-2x^{3-1}-y^2=3^2\)

 

Answer 2

\(x^2+y^2-2x+y=9\)

\(\Leftrightarrow4x^2+4y^2-8x+4y=36\)

\(\Leftrightarrow4x^2-8x+4+4y^2+4y+1=41\)

\(\Leftrightarrow\left(2x-2\right)^2+\left(2y+1\right)^2=41\)

Vì \(\left(2x-2\right)^2\ge0\) với \(\forall x\)

\(\Rightarrow\left(2y+1\right)^2\le41\)

Mà \(\left(2y+1\right)^2\) là số lẻ \(\Rightarrow\left(2y+1\right)^2\in\left\{1;9;25\right\}\)

\(\Rightarrow y\in\left\{0;1;2;-1;-2;-3\right\}\)

Tìm được y rồi thì thay vào tìm x nhé.