let j=e^((i2π)/3) and P(x)=(1+jx)^n −(1−jx)^n with n integr natural 1) find roots of P(x) 2)factorize P(x) inside C[x] 3) calculate ∫_0 ^1 P(x)dx. 4) decompose inside C(x) the fraction F(x)=(1/(P(x)))


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Question Number 52449 by maxmathsup by imad last updated on 07/Jan/19
$let j=e^((i2π)/3) and P(x)=(1+jx)^n −(1−jx)^n with n integr natural 1) find roots of P(x) 2)factorize P(x) inside C[x] 3) calculate ∫_0 ^1 P(x)dx. 4) decompose inside C(x) the fraction F(x)=(1/(P(x)))$
$l e t j = e^{\frac{i 2 π}{3}} a n d P (x) = {(1 + j x)}^{n} - {(1 - j x)}^{n} w i t h n i n t e g r n a t u r a l$ $1) f i n d r o o t s o f P (x)$ $2) f a c t o r i z e P (x) i n s i d e C [x]$ $3) c a l c u l a t e \int_{0}^{1} P (x) d x .$ $4) d e c o m p o s e i n s i d e C (x) t h e f r a c t i o n F (x) = \frac{1}{P (x)}$
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