若多项式x²-2x+3=A(x+1)²+B(x+1)+C其中ABC为常数,求A+B+C的值
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![若多项式x²-2x+3=A(x+1)²+B(x+1)+C其中ABC为常数,求A+B+C的值](/uploads/image/z/3011181-69-1.jpg?t=%E8%8B%A5%E5%A4%9A%E9%A1%B9%E5%BC%8Fx%26%23178%3B-2x%2B3%3DA%EF%BC%88x%2B1%EF%BC%89%26%23178%3B%2BB%EF%BC%88x%2B1%EF%BC%89%2BC%E5%85%B6%E4%B8%ADABC%E4%B8%BA%E5%B8%B8%E6%95%B0%2C%E6%B1%82A%2BB%2BC%E7%9A%84%E5%80%BC)
若多项式x²-2x+3=A(x+1)²+B(x+1)+C其中ABC为常数,求A+B+C的值
若多项式x²-2x+3=A(x+1)²+B(x+1)+C其中ABC为常数,求A+B+C的值
若多项式x²-2x+3=A(x+1)²+B(x+1)+C其中ABC为常数,求A+B+C的值
解由x²-2x+3
=x²+2x+1-2x-2x+3-1
=(x+1)²-2x-2x+3-1
=(x+1)²-4x+2
=(x+1)²-4x-8+8+2
=(x+1)²-4(x+2)+10
=A(x+1)²+B(x+1)+C
即A=1,B=-4,C=10
即A+B+C
=1+(-4)+10
=7