if a+b+c=0 then prove 1/x^b+x^-c+1+1/x^c+x^-a+1+1/x^a+x^-b+1=1
Answers
Answered by
0
Answer:
Formula:
x
m−n
=
x
n
x
m
LHS=
1+x
b−a
+x
c−a
1
+
1+x
a−b
+x
c−b
1
+
1+x
b−c
+x
a−c
1
=
1+
x
a
x
b
+
x
a
x
c
1
+
1+
x
b
x
a
+
x
b
x
c
1
+
1+
x
c
x
b
+
x
c
x
a
1
=
x
a
+x
b
+x
c
x
a
+
x
b
+x
a
+x
c
x
b
+
x
c
+x
b
+x
a
x
c
=
x
a
+x
b
+x
c
x
a
+x
b
+x
c
=1=RHS
Hence proof.
Answered by
0
Answer:
1
Step-by-step explanation:
=(1/x^b+x^-c+1 × x^-b/ x^-b )+(1/x^c+x^-a+1 × x^a/x^a)+(1/x^a+x^-b+1)
=(x^-b/x^0+x^-b-c+x^-b) + (x^a/x^a+c+x^0+x^a)+ (1/x^a+x^-b+1)
=x^-b/1+x^a+x^-b + x^a/x^-b+x^a+1 + 1/x^a+x^-b+1
=x^a+x^-b+1 / x^a+x^-b+1
=1
[Prove]
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