-x^2+x^10 = a0+a1(x+1)+.+a9(x+1)^9+a10(x+1)^10,a10=1,x^9系数=0 ,求a9,答案是a9=-10,是 x^2+x^10 = a0+a1(x+1)+......+a9(x+1)^9+a10(x+1)^10,a10=1
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![-x^2+x^10 = a0+a1(x+1)+.+a9(x+1)^9+a10(x+1)^10,a10=1,x^9系数=0 ,求a9,答案是a9=-10,是 x^2+x^10 = a0+a1(x+1)+......+a9(x+1)^9+a10(x+1)^10,a10=1](/uploads/image/z/3976239-39-9.jpg?t=-x%5E2%2Bx%5E10+%3D+a0%2Ba1%28x%2B1%29%2B.%2Ba9%28x%2B1%29%5E9%2Ba10%28x%2B1%29%5E10%2Ca10%3D1%2Cx%5E9%E7%B3%BB%E6%95%B0%3D0+%2C%E6%B1%82a9%2C%E7%AD%94%E6%A1%88%E6%98%AFa9%3D-10%2C%E6%98%AF+x%5E2%2Bx%5E10+%3D+a0%2Ba1%28x%2B1%29%2B......%2Ba9%28x%2B1%29%5E9%2Ba10%28x%2B1%29%5E10%2Ca10%3D1)
-x^2+x^10 = a0+a1(x+1)+.+a9(x+1)^9+a10(x+1)^10,a10=1,x^9系数=0 ,求a9,答案是a9=-10,是 x^2+x^10 = a0+a1(x+1)+......+a9(x+1)^9+a10(x+1)^10,a10=1
-x^2+x^10 = a0+a1(x+1)+.+a9(x+1)^9+a10(x+1)^10,a10=1,x^9系数=0 ,求a9,答案是a9=-10,
是 x^2+x^10 = a0+a1(x+1)+......+a9(x+1)^9+a10(x+1)^10,a10=1
-x^2+x^10 = a0+a1(x+1)+.+a9(x+1)^9+a10(x+1)^10,a10=1,x^9系数=0 ,求a9,答案是a9=-10,是 x^2+x^10 = a0+a1(x+1)+......+a9(x+1)^9+a10(x+1)^10,a10=1
左边x^9系数为0,所以右边x^9系数也要为0.
右边能出现x^9的其实就是最后两项,因为前面的比如a5(x+1)^5,它乘出来最多只可能出现x^5,没有x^9的.
所以x^9只会出现在a9(x+1)^9和(x+1)^10里.
a9(x+1)^9里面,很显然,x^9的系数就是a9
(x+1)^10里面,用二项式定理,x^9的系数是C(10,1)=10
所以a9+10要等于0
a9=-10
把a10=1,带入等式:x^2+x^10 = a0+a1(x+1)+......+a9(x+1)^9+(x+1)^10,
x^2+x^10 = a0+a1(x+1)+......+a9(x+1)^9+x^10+10x^9+....,
把x^9系数整理出来:(a9+10),根据已知x^9系数=0,所以a9=-10
左边x^9的系数=0
右边x^9的系数=a9*1+a10*10
已知a10=1
则a9+10*1=0
a9=-10