Q: The value of 1/(x^b + x^-c + 1) +1/( x^c + x^-a + 1) + 1/(x^a + x^-b + 1) , given that a + b + c = 0 , is :
a)1
b)0
c)abc
d)x
e)xyz
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Algebra - 1
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Aman verma
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1/(x^b + x^-c + 1) = x^c/(x^(b + c) + 1 + x^c) = x^c/(x^-a + 1 + x^c) ; because [b + c = -a]The value of 1/(x^b + x^-c + 1) +1/( x^c + x^-a + 1) + 1/(x^a + x^-b + 1) , given that a + b + c = 0 , is :
1/(x^a + x^-b + 1) = x^(b + c)/(x^(a + b+ c) + x ^c + x^(b + c)) = x^-a/(1 + x^c + x^-a)
Add all three term
denominator is same
( 1 + x^c + x^-a)/(1 + x^c + x^-a) = 1
Hence Ans.
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Aman verma
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1/(x^b + x^-c + 1) = 1/(x^b + (1/x^c )+ 1) = 1//((x^b)(x^c) + 1 + x^c)/x^c = x^c/(x^(b + c) + 1 + x^c)um can anyone out there explain the above post. I'm having troubles understanding how
1/(x^b + x^-c + 1) = x^c/(x^(b + c) + 1 + x^c) = x^c/(x^-a + 1 + x^c) ;
= x^c/(x^-a + 1 + c^c) [b + c = -a given in question]
Hope you will get now
