若x^2-6x-2的2倍减去一个多项式得4x^2-7x-5,则这个多项式为________.3.已知A=a^2+b^2-c^2,B=-4a^2+2b^2+3c^2,若A+B+C=0,则C=________.
问题描述:
若x^2-6x-2的2倍减去一个多项式得4x^2-7x-5,则这个多项式为________.
3.已知A=a^2+b^2-c^2,B=-4a^2+2b^2+3c^2,若A+B+C=0,则C=________.
答
2(x^2-6x-2)-(4x^2-7x-5)
=2x^2-12x-4-4x^2+7x+5
= -2x^2-5x+1
A+B+C=a^2+b^2-c^2-4a^2+2b^2+3c^2+C
=-3a^2+3b^2+2c^2+C=0
C=3a^2-3b^2-2c^2