It is given that
(1-2x+3x^2)^n=1-10x+kx^2 + terms involving higher powers of x,
where n is a positive integer and k is a constant. Find the values of n and k. (5 marks)
binomial theorem SHORT QUESTION @ 2006 A.Maths CE
2006-10-16 3:38 am
回答 (1)
2006-10-16 3:44 am
✔ 最佳答案
(1-2x+3x^2)^n=1-10x+kx^2 + terms involving higher powers of x,(1+x(3x-2))^n=1-10x+kx^2 + terms involving higher powers of x
1+nx(3x-2)+[(n(n-1)/2][x(3x-2)]^2+...=1-10x+kx^2 + terms involving higher powers of x
1+nx(3x-2)+[(n(n-1)/2][x(3x-2)]^2=1-10x+kx^2+...
1+3nx^2-2nx+[(n(n-1)/2][4x^2]=1-10x+kx^2
1+3nx^2-2nx+[(n(n-1)][2x^2]=1-10x+kx^2
-2n=-10
3n+2(n)(n-1)=k
n=5
k=15+2*5*4
k=55
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