if a+b+c=0 then find the value of x^a+b-c.x^b+c-a.x^c+a-b
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Answer:
(x
a
)
a
2
−bc
.(x
b
)
b
2
−ca
.(x
c
)
c
2
−ab
Then,
(x
a
)
a
2
−bc
.(x
b
)
b
2
−ca
.(x
c
)
c
2
−ab
⇒x
a
3
−abc
.x
b
3
−cab
.x
c
3
−abc
⇒x
a
3
−abc+b
3
−abc+c
3
−abc
⇒x
a
3
+b
3
+c
3
−3abc
⇒x
(a+b+c)(a
2
+b
2
+c
2
−ab−bc−ca)
⇒x
0×(a
2
+b
2
+c
2
−ab−bc−ca)
⇒x
0
=1
Hence, this is the answer.
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