Bonsoir,
[tex]x^2+xy+y^2=4 ==\ \textgreater \ \\
(x+y)^2=4+xy\\
(x-y)^2=4-3xy\\
x^4+x^2y^2+y^4=8==\ \textgreater \ \\
(x^2+y^2)^2=8+x^2y^2\\
(4-xy)^2=8+x^2y^2==\ \textgreater \ 16-8xy+x^2y^2=8+x^2y^2 ==\ \textgreater \ xy=1\\
x+y= \sqrt{4+1} \\
x-y=1\\
x= \dfrac{1+ \sqrt{5} }{2} \\
y =\dfrac{-1+ \sqrt{5} }{2} \\
x^2= \frac{3+ \sqrt{5} }{2} \\
x^4= \frac{7+ 3\sqrt{5} }{2} \\
x^6=9+4 \sqrt{5}
y^4= \frac{1}{x^4} = \frac{7-3 \sqrt{5} }{2} \\
x^6+x^3y^3+y^4= \frac{27+ 5\sqrt{5} }{2}=7.9093300... \\
[/tex]
