The binomial expansion of (1+px)n, where n>0, in ascending powers of x is
1 - 12x + 28p²x² + qx³+ ...
Find n, p, and q
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Answer:
(1+px)n
= 1 + npx + [n(n-1)/2]p²x² + [n(n-1)(n-2)/6]p³x³+ ...
= 1 - 12x + 28p²x² + qx³+ ...
By comparing,
np = -12 -----------------(1)
[n(n-1)/2]p²= 28p² ------(2)
[n(n-1)(n-2)/6]p³ = q ----(3)
From (2):
n² - n= 56
n² - n - 56 = 0
(n-8)(n+7)=0
n=8 or -7 (rej. as n>0)
sub n=8 into (1):
8p = -12
p= -1.5
sub n=8 into (3):
8×7×6×(-27/8) / 6 = q
q = 56×-(27/8)
= -189
