If a+b+c=0, then {1}/{x^{a}+x^{-b}+1}+{1}/{x^{b}+x^{-c}+1}+{1}/{x^{c}+x^{-a}+1}=

AP ICET 2016 Paper

Question : 84 of 200

Marks: +1, -0

a+b+c=0,

then

{1}/{x^{a}+x^{-b}+1}+{1}/{x^{b}+x^{-c}+1}+{1}/{x^{c}+x^{-a}+1}=

Solution:

Given : a + b + c = 0

{1}/{x^{a}+x^{-b}+1}+{1}/{x^{b}+x^{-c}+1}+{1}/{x^{c}+x^{-a}+1}

={x^{b}}/{x^{a+b}+1+x^{b}}+{1}/{x^{b}+x^{-c}+1}+{1}/{x^{c+a}+1+x^{a}}

={x^{b}}/{x^{-c}+1+x^{b}}+{1}/{x^{b}+x^{-c}+1}+{x^{a}}/{x^{-b}+1+x^{a}}×({x^{b}}/{x^{b}})

={x^{b}}/{1+x^{b}+x^{-c}}+{1}/{1+x^{b}+x^{-c}}+{x^{-c}}/{1+x^{b}+x^{-c}}

[Using a + b = – c]

={x^b+1+x^{-c}}/{1+x^b+x^{-c}}=1

[Answer choice 3]
Answer choice (1) :

x^{a+b+c}=x^{0}=1[a+b+c=0]

Go to Question:

Prev Question

Next Question