Question

Giải phương trình nghiệm nguyên: 5x⁴ + y² - 4x²y - 85 = 0

Answer 1

\(5x^4+y^2-4x^2y-85=0\)

\(\Leftrightarrow\left(4x^4-4x^2y+y^2\right)+x^4=85\)

\(\Leftrightarrow\left(2x^2-y\right)^2+x^4=85\)\(\left(=2^2+3^4\right)\)

\(\Rightarrow\left\{{}\begin{matrix}x=3\\\left|2x^2-y\right|=2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=3\\18-y=\pm2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=3\\\left[{}\begin{matrix}y=16\\y=20\end{matrix}\right.\end{matrix}\right.\left(n\right)\)

Vậy . . . >///<