已知(x^2-3x+1)^5=ax^5+bx^4+cx^3+dx^2+ex+f,求a+c+e
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已知(x^2-3x+1)^5=ax^5+bx^4+cx^3+dx^2+ex+f,求a+c+e
![已知(x^2-3x+1)^5=ax^5+bx^4+cx^3+dx^2+ex+f,求a+c+e](/uploads/image/z/2997447-15-7.jpg?t=%E5%B7%B2%E7%9F%A5%28x%5E2-3x%2B1%29%5E5%3Dax%5E5%2Bbx%5E4%2Bcx%5E3%2Bdx%5E2%2Bex%2Bf%2C%E6%B1%82a%2Bc%2Be)
x=1时
(1-3+1)^5=a+b+c+d+e+f
∴a+b+c+d+e+f=-1 (1)
当x=-1时
(1+3+1)^5=-a+b-c+d-e+f
∴-a+b-c+d-e+f=5^5 (2)
(1)-(2)得
2a+2c+2e=-1-3125
∴a+c+e=-1563
(1-3+1)^5=a+b+c+d+e+f
∴a+b+c+d+e+f=-1 (1)
当x=-1时
(1+3+1)^5=-a+b-c+d-e+f
∴-a+b-c+d-e+f=5^5 (2)
(1)-(2)得
2a+2c+2e=-1-3125
∴a+c+e=-1563
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