If x^a+b=x^-c then what's the value of a³+b³+c³?
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Answer:
here your answer
Step-by-step explanation:
(a−b)(a−c)(x−a)
a
+
(b−c)(b−a)(x−b)
b
+
(c−a)(c−b)(x−c)
c
=
(a−b)(a−c)(x−a)
a
−
(b−c)(a−b)(x−b)
b
+
(c−a)(c−b)(x−c)
c
=
(a−b)(a−c)(b−c)(x−a)(x−b)(x−c)
a(b−c)(x−b)(x−c)−b(a−c)(x−a)(x−c)+c(a−b)(x−a)(x−b)
expanding numerator and denominator, we get
=
(a
2
b−a
2
c−abc+ac
2
−ab
2
+abc+b
2
c−bc
2
)(x−a)(x−b)(x−c)
(ab−ac)(x
2
−xc−xb+bc)−(ab−bc)(x
2
−xc−xa+ac)+(ac−bc)(x
2
−xb−xa+ab)
=
(a
2
b−a
2
c+ac
2
−ab
2
+b
2
c−bc
2
)(x−a)(x−b)(x−c)
x(a
2
b−a
2
c+ac
2
−ab
2
+b
2
c−bc
2
)
=
(x−a)(x−b)(x−c)
x
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