For KVPY

Algebra Level 3

Let S denotes the set of all real values of x such that ∑ P = 0 P = K x 2 P = ( 2 K + 2 ) x 2 K + 2 x ( x 2 K + 2 + 1 ) \sum_{P=0}^{P=K} x^{2P} = \dfrac{(2K+2) x^{2K+2}}{x(x^{2K+2} + 1)} holds true for some positive integer k . Find the number of elements in the set S. If u think Number of elements depend on k enter 2016


The answer is 1.

Gauri shankar Mishra by Gauri shankar Mishra , 21, India

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1 solution

i'll write a sol. then, put k+1=z; simplify LHS by using the summation formula of G.P ow reduce the expression to the least you can i terms of z , it will not be very tough to show that the expression is independent of z itself , now solve the cubic eqn u get, it would have only 1 positive sol. for x , other 2 roots are complex! u just got the answer good question by G a u r i s h a n k a r m i s h r a Gauri \ shankar\ mishra i'm not good at latex! so just stand by plz !

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