nonlinear newton method no matlab

Hi everyone.

I need help with this exercise as I can't figure out how to do it.

Thanks to anyone who will help me.

Given the following system of non linear equations:

{4x(x^2 + y^2) +3y =0

{4y(x^2 + y^2) +3x =0

Verify that the given sustem has three solutions in D=[-2,2] x [-2,2] by suitably motivating the answer and determining the values

Thank you