Consider finding an approximate solution to the nonlinear system of equations 2x 1 − x 2 2 = 0, x 1 + 0.77x 2 = 1, where x (0) = 0. (a) Apply one iteration of the Newton method to obtain x (1) (b)...

Consider finding an approximate solution to the nonlinear system of equations
2x₁
− x²
₂ = 0,
x₁
+ 0.77x₂
= 1,
where x⁽⁰⁾ = 0.
(a) Apply one iteration of the Newton method to obtain x⁽¹⁾

(b) Redo the previous part but by applying one iteration of the steepest descent
method.