Question

find the value with complete explanation

Answer 1

let
( a - b) = P , => ( b -a) = - P
(b - c) = q , => ( c - b) = -q
(c -a) = r , => ( a - c) = -r
hence,
P + q + r = (a - b) + ( b -c) + (c -a) =0
P + q + r = 0

so, question now , convert into
1/( 1+ x^-P + x^r) + 1/( 1+ x^p + x^-q) + 1/( 1+ x^q + x^-r )

now,

1/( 1+ 1/x^p + x^r) = x^p/{x^p + 1 + x^( p+r)}

= x^p/{ x^p + 1 + x^( -q)} { from P+r = -q}

= x^(p+q)/{ x^(P+q) +x^q + 1 }

= x^-r/( x^-r + x^q + 1 )

similarly,

1/( 1+ x^p+ x^-q) = x^q/( x^q + x^(P+q) + 1)

= x^q/{ x^q + x^-r + 1) { from P+q = -r

put this value above ,

x^-r/( x^-r + x^q + 1) + x^q/( x^q + x^-r+1) +1/( 1+ x^q + x^-r)

= ( x^-r + x^q + 1)/( x^-r + x^q +1)

= 1

Answer 2

Answer:

answer refer in pic

Step-by-step explanation:

hope it will helps you