初高中数学衔接 繁分式 已知(x²+x-3)\[(x-1)(x-2)(x-3)]=A\(x-1)+B\(x-2)+C\(x-3),求A,B,C的再问一次,刚刚太激动了,答案给的在详细点则x^+ x - 3=A(x^-5x+6)+B(x^-4x+3)+C(x^-3x+2)???如何得到三个
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![初高中数学衔接 繁分式 已知(x²+x-3)\[(x-1)(x-2)(x-3)]=A\(x-1)+B\(x-2)+C\(x-3),求A,B,C的再问一次,刚刚太激动了,答案给的在详细点则x^+ x - 3=A(x^-5x+6)+B(x^-4x+3)+C(x^-3x+2)???如何得到三个](/uploads/image/z/1329579-27-9.jpg?t=%E5%88%9D%E9%AB%98%E4%B8%AD%E6%95%B0%E5%AD%A6%E8%A1%94%E6%8E%A5+%E7%B9%81%E5%88%86%E5%BC%8F+%E5%B7%B2%E7%9F%A5%EF%BC%88x%26sup2%3B%2Bx-3%EF%BC%89%5C%5B%EF%BC%88x-1%EF%BC%89%EF%BC%88x-2%EF%BC%89%EF%BC%88x-3%EF%BC%89%5D%3DA%5C%28x-1%29%2BB%5C%28x-2%29%2BC%5C%28x-3%29%2C%E6%B1%82A%2CB%2CC%E7%9A%84%E5%86%8D%E9%97%AE%E4%B8%80%E6%AC%A1%2C%E5%88%9A%E5%88%9A%E5%A4%AA%E6%BF%80%E5%8A%A8%E4%BA%86%2C%E7%AD%94%E6%A1%88%E7%BB%99%E7%9A%84%E5%9C%A8%E8%AF%A6%E7%BB%86%E7%82%B9%E5%88%99x%5E%2B+x+-+3%3DA%28x%5E-5x%2B6%29%2BB%28x%5E-4x%2B3%29%2BC%28x%5E-3x%2B2%29%EF%BC%9F%EF%BC%9F%EF%BC%9F%E5%A6%82%E4%BD%95%E5%BE%97%E5%88%B0%E4%B8%89%E4%B8%AA)
初高中数学衔接 繁分式 已知(x²+x-3)\[(x-1)(x-2)(x-3)]=A\(x-1)+B\(x-2)+C\(x-3),求A,B,C的再问一次,刚刚太激动了,答案给的在详细点则x^+ x - 3=A(x^-5x+6)+B(x^-4x+3)+C(x^-3x+2)???如何得到三个
初高中数学衔接 繁分式 已知(x²+x-3)\[(x-1)(x-2)(x-3)]=A\(x-1)+B\(x-2)+C\(x-3),求A,B,C的
再问一次,刚刚太激动了,答案给的在详细点
则x^+ x - 3=A(x^-5x+6)+B(x^-4x+3)+C(x^-3x+2)
???如何得到三个方程
A+B+C=1, -5A-4B-3C=1, 6A+3B+2C=-3
初高中数学衔接 繁分式 已知(x²+x-3)\[(x-1)(x-2)(x-3)]=A\(x-1)+B\(x-2)+C\(x-3),求A,B,C的再问一次,刚刚太激动了,答案给的在详细点则x^+ x - 3=A(x^-5x+6)+B(x^-4x+3)+C(x^-3x+2)???如何得到三个
将右式通分,分子为(A+B+C)X2-(5A+4B+3C)X+(6A+3B+2C)
于是可得A+B+C=1 5A+4B+3C=-1 6A+3B+2C=-3
说到这就能明白了吧,解三元方程组就可得ABC的值
( x^+ x - 3 ) / ( (x-1) (x-2) (x-3) )
=A / (X-1)+B/ ( X-2) + C/ (x - 3 )
=[A(x^-5x+6)+B(x^-4x+3)+C(x^-3x+2)]/[(x-1)(x-2)(x-3)]
则x^+ x - 3=A(x^-5x+6)+B(x^-4x+3)+C(x^-3x+2)
得到三个方程
A+B+C=1, -5A-4B-3C=1, 6A+3B+2C=-3
结果为
A=-1/2, B=-3, C=9/2