Hii !
Can You Help Me in This System,
Solve in $\displaystyle \mathbb{R}^2$ The System :
$\displaystyle \left\{\begin{array}{rcl}
x^3y=9 \\ 3x + y = 6
\end{array}\right.
$
Hi
$\displaystyle y = \frac{9}{x^3}$
$\displaystyle 3x + \frac{9}{x^3} = 6$
$\displaystyle x^4 - 2x^3 + 3 = 0$
$\displaystyle f(x) = x^4 - 2x^3 + 3$ is decreasing over ]-oo,3/2] and increasing over [3/2,+oo[ and f(3/2) = 21/16 > 0
Therefore f(x) > 0 for all x and there are no solutions