Ta có : $\left\{ \begin{array}{l}x^2+y^2=5\\x^4+y^4+x^2y^2=13\end{array} \right. $
$⇔\left\{ \begin{array}{l}x^2+y^2=5\\(x^2+y^2)^2-x^2y^2=13\end{array} \right. $
$⇔\left\{ \begin{array}{l}x^2+y^2=5\\5^2-x^2y^2=13\end{array} \right. $
$⇔\left\{ \begin{array}{l}x^2+y^2=5\\x^2y^2=12\end{array} \right. $
$⇔\left\{ \begin{array}{l}x^2+y^2=5\\x^2=\dfrac{12}{y^2}\end{array} \right. $
$⇒ \dfrac{12}{y^2}+y^2=5$
$⇔y^4-5y^2+12=0$
$⇔\bigg(y^2-\dfrac{5}{2}\bigg)^2+\dfrac{23}{4}=0$ ( Vô nghiệm )
Vậy hệ phương trình đã cho vô nghiệm.
