\(\left\{{}\begin{matrix}u^2+v^2=13\\uv=16\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}u^2+v^2=13\\u^2v^2=256\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}u^2=13-v^2\\\left(13-v^2\right)v^2=256\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}u^2=13-v^2\\13v^2-v^4-256=0\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}u^2=13-v^2\\v^4-13v^2+256=0\left(1\right)\end{matrix}\right.\)
(1) \(\Leftrightarrow\) v4 - 2.\(\dfrac{13}{2}\)v2 + \(\dfrac{169}{4}\) + \(\dfrac{855}{4}\) = 0
\(\Leftrightarrow\) (v2 - \(\dfrac{13}{2}\))2 + \(\dfrac{855}{4}\) = 0 (Vô nghiệm)
\(\Rightarrow\) Pt vô nghiệm
\(\Rightarrow\) Hpt vô nghiệm
Chúc bn học tốt!
