Question :
If the roots of the equation ( a − b ) ² + ( b − c ) ² + ( c − a )² = 0 are equal, prove that 2 a = b + c .Submitted on 8/3/2024 | Answered by Vandana Rana
Answer :
Given,
(
a
−
b
)
x2
+
(
b
−
c
)
x
+
(
c
−
a
)
=
0
are equal.
Then the discriminant (D)
=
0
Then
(
b
−
c
)2
−
4
(
c
−
a
)
(
a
−
b
)
=
0
b2
−
2
b
c
+
c2
−
4
(
a
c
−
b
c
−
a2
+
a
b
)
=
0
b2
2
b
c
+
c2
−
4ac + 4bc + 4a2 - 4
ab=0
b2 + c2 + 4a2 + 2bc - 4ac - 4ab =0
(
b
+
c
−
2
a
)2
=
0
2
a
=
b
+
c