given (1+4x+x^2)^n=1+ax+bx^2+other terms involving higher powers of x
where n is +ve integer
1.express a and b in term of n
2.if a=20 find n and b
F.4 AMATH
2007-11-01 8:42 am
回答 (1)
2007-11-01 9:27 am
✔ 最佳答案
1. (1+4x+x^2)^n
=[1 + x(4 + x)]^n
= 1 + nx(4 + x) + [n(n - 1) / 2][x(4 + x)]^2 + ...
= 1 + nx(4 + x) + [n(n - 1) / 2][x^2(16 + 8x + x^2)] + ...
= 1 + nx(4 + x) + [n(n - 1) / 2](16x^2) + ...
= 1 + 4nx + [n + 16n(n - 1) / 2]x^2 + ...
So a=4n, b=n + 16n(n - 1) / 2
2
a=4n =20, n=5
b=n + 16n(n - 1) / 2= 5 + 16*5(5 - 1) / 2=165
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