Encontrar raices de las ecuaciones simultaneas [ ]
(
X
−
4
)
2
+
(
y
−
4
)
2
=
5
{\displaystyle (X-4)^{2}+(y-4)^{2}=5}
(
x
−
h
)
2
+
(
y
−
k
)
2
>
r
2
{\displaystyle (x-h)^{2}+(y-k)^{2}>r^{2}}
Datos iniciales por ejemplo
X
0
=
1
,
y
=
4
{\displaystyle X0=1,y=4}
Deducir metodo de newton para ejemplo
Linealizar
u
,
v
{\displaystyle u, v}
x
0
,
y
0
{\displaystyle x_0, y_0}
Calcular el cero de la linealizacion
w
(
x
,
y
)
=
(
x
−
4
)
2
+
(
y
−
4
)
2
−
5
=
0
{\displaystyle w(x,y)=(x-4)^{2}+(y-4)^{2}-5=0}
v
(
x
,
y
)
=
x
2
+
y
2
−
16
=
0
{\displaystyle v(x,y)=x^{2}+y^{2}-16=0}
u
i
+
1
=
[
(
x
−
4
)
2
+
(
y
−
4
)
2
−
5
]
+
2
(
x
−
4
)
+
2
(
y
−
4
)
{\displaystyle u_{i+1}=[(x-4)^{2}+(y-4)^{2}-5]+2(x-4)+2(y-4)}
u
(
x
i
+
1
,
y
i
+
1
)
=
u
(
x
i
,
y
i
)
+
∂
u
(
x
i
,
y
i
)
∂
λ
(
λ
i
+
1
+
x
i
)
.
.
.
.
+
∂
u
(
x
i
,
y
i
)
∂
y
(
y
i
+
1
+
y
i
)
{\displaystyle u(x_{i}+1,y_{i}+1)=u(x_{i},y_{i})+{\frac {\partial u(x_{i},y_{i})}{\partial \lambda }}(\lambda _{i+1}+x_{i})....+{\frac {\partial u(x_{i},y_{i})}{\partial y}}(y_{i+1}+y_{i})}
<math>v_{i+1} = (x^2 + y^2 -16) +2x +2y = 0
![{\displaystyle u_{i+1}=[(x-4)^{2}+(y-4)^{2}-5]+2(x-4)+2(y-4)}](https://services.fandom.com/mathoid-facade/v1/media/math/render/svg/f9ead9e29893a97739c491b39140ac3043f26a09)
