Advanced System Of Equations

Algebra Level 5

How many ordered pairs of real numbers (x,y) (x,y) are there such that

{x2y2+πx+ϕyx2+y2=2,2xy+ϕxπyx2+y2=0. \begin{cases} x^2 - y^2 & + \frac{\pi x+\phi y}{x^2+y^2} & = \sqrt{2}, \\ 2xy & + \frac{ \phi x-\pi y}{x^2 + y^2} & = 0. \\ \end{cases}

( ϕ \phi is the golden ratio 1+52 \frac{1+ \sqrt{5} } { 2} . π \pi is pi, which is approximately 3.14159 3.14159 .)

×

Problem Loading...

Note Loading...

Set Loading...