If a + b + c = 1, ab + bc + ca = 2 and abc = 3, then the value of a4 + b4 + c4 is equal to
∵
a
2
+
b
2
+
c
2
=
(
a
+
b
+
c
)
2
−
2
(
a
b
+
b
c
+
c
a
)
∴
a
2
+
b
2
+
c
2
=
1
−
4
=
−
3
and
a
2
b
2
+
b
2
c
2
+
c
2
a
2
=
(
a
b
+
b
c
+
c
a
)
2
−
2
a
b
c
(
a
+
b
+
c
)
a
2
b
2
+
b
2
c
2
+
c
2
a
2
=
4
−
6
=
−
2
Now,
a
4
+
b
4
+
c
4
=
(
a
2
+
b
2
+
c
2
)
2
−
2
(
a
2
b
2
+
b
2
c
2
+
c
2
a
2
)
⇒
a
4
+
b
4
+
c
4
=
9
+
4
∴
a
4
+
b
4
+
c
4
=
13
