27
Ecuaciones bicuadradas
Ecuaciones
.
Resuelve las ecuaciones bicuadradas propuestas.
a)
x
4
−
34
x
2
+
225
=
0
b)
x
4
−
65
x
2
+
784
=
0
c)
x
4
−
7
x
2
+
12
=
0
d)
x
4
−
8
x
2
−
9
=
0
Para deshacer el cambio de variable,
igualamos
x
2
a los valores obtenidos.
Presta atención
x
2
=
p
→
p
2
−
34
p
+
225
=
0
→
a
=
1,
b
=
−
34,
c
=
225
p
=
34
±
(
−
34 )
2
−
4
⋅
1
⋅
225
2
⋅
1
=
34
±
256
2
=
34
±
16
2
→
p
=
34
+
16
2
=
25
p
=
34
−
16
2
=
9
⎧
⎨
⎪⎪⎪⎪⎪
⎩
⎪⎪⎪⎪⎪
x
2
=
25
→
x
= ±
25
→
x
=
5
x
=
−
5
⎧
⎨
⎪⎪
⎩⎪⎪
x
2
=
9
→
x
= ±
9
→
x
=
3
x
=
−
3
⎧
⎨
⎪⎪
⎩⎪⎪
x
2
=
p
→
p
2
−
65
p
+
784
=
0
→
a
=
1,
b
=
−
65,
c
=
784
p
=
65
±
(
−
65)
2
−
4
⋅
1
⋅
784
2
⋅
1
=
65
±
1089
2
=
65
±
33
2
→
p
=
65
+
33
2
=
49
p
=
65
−
33
2
=
16
⎧
⎨
⎪⎪⎪⎪⎪
⎩
⎪⎪⎪⎪⎪
x
2
=
49
→
x
= ±
49
→
x
=
7
x
=
−
7
⎧
⎨
⎪⎪
⎩⎪⎪
x
2
=
16
→
x
= ±
16
→
x
=
4
x
=
−
4
⎧
⎨
⎪⎪
⎩⎪⎪
x
2
=
p
→
p
2
−
7
p
+
12
=
0
→
a
=
1,
b
=
−
7,
c
=
12
p
=
7
±
(
−
7)
2
−
4
⋅
1
⋅
12
2
⋅
1
=
7
±
49
−
48
2
=
7
±
1
2
=
7
±
1
2
→
p
=
7
+
1
2
=
4
p
=
7
−
1
2
=
3
⎧
⎨
⎪⎪⎪⎪⎪
⎩
⎪⎪⎪⎪⎪
x
2
=
4
→
x
= ±
4
→
x
=
2
x
=
−
2
⎧
⎨
⎪⎪
⎩⎪⎪
x
2
=
3
→
x
= ±
3
→
x
=
3
x
=
−
3
⎧
⎨
⎪⎪
⎩
⎪⎪
x
2
=
p
→
p
2
−
8
p
−
9
=
0
→
a
=
1,
b
=
−
8,
c
=
−
9
p
=
8
±
(
−
8)
2
−
4
⋅
1
⋅
(
−
9)
2
⋅
1
=
8
±
64
+
36
2
=
8
±
100
2
=
8
±
10
2
→
p
=
8
+
10
2
=
9
p
=
8
−
10
2
=
−
1
⎧
⎨
⎪⎪⎪⎪⎪
⎩
⎪⎪⎪⎪⎪
x
2
=
9
→
x
= ±
9
→
x
=
3
x
=
−
3
⎧
⎨
⎪⎪
⎩⎪⎪
x
2
=
−
1
→
x
= ±
−
1
→
No son soluciones reales, porque el resultado es la raíz cuadrada
de un número negativo.
