해법
(x2+ax+2)(x+3)=(x+b)(x2+cx+6)
해법
x=2(a−b−c+3)−3a+bc+4+b2c2−24b2+24ab+96b−6abc−16bc+9a2+24c−48a−56,x=2(a−b−c+3)−3a+bc+4−b2c2−24b2+24ab+96b−6abc−16bc+9a2+24c−48a−56;a−b−c+3=0
솔루션 단계
(x2+ax+2)(x+3)=(x+b)(x2+cx+6)
(x2+ax+2)(x+3) 확장 :x3+3x2+ax2+3ax+2x+6
(x+b)(x2+cx+6) 확장 :x3+cx2+6x+bx2+bcx+6b
x3+3x2+ax2+3ax+2x+6=x3+cx2+6x+bx2+bcx+6b
빼다 x3+cx2+6x+bx2+bcx+6b 양쪽에서x3+3x2+ax2+3ax+2x+6−(x3+cx2+6x+bx2+bcx+6b)=x3+cx2+6x+bx2+bcx+6b−(x3+cx2+6x+bx2+bcx+6b)
단순화
(a−b−c+3)x2+(3a−bc−4)x−6b+6=0
쿼드 공식으로 해결
x1,2=2(a−b−c+3)−(3a−bc−4)±(3a−bc−4)2−4(a−b−c+3)(−6b+6)
(3a−bc−4)2−4(a−b−c+3)(−6b+6)단순화하세요:b2c2−24b2+24ab+96b−6abc−16bc+9a2+24c−48a−56
x1,2=2(a−b−c+3)−(3a−bc−4)±b2c2−24b2+24ab+96b−6abc−16bc+9a2+24c−48a−56;a−b−c+3=0
솔루션 분리x1=2(a−b−c+3)−(3a−bc−4)+b2c2−24b2+24ab+96b−6abc−16bc+9a2+24c−48a−56,x2=2(a−b−c+3)−(3a−bc−4)−b2c2−24b2+24ab+96b−6abc−16bc+9a2+24c−48a−56
x=2(a−b−c+3)−(3a−bc−4)+b2c2−24b2+24ab+96b−6abc−16bc+9a2+24c−48a−56:2(a−b−c+3)−3a+bc+4+b2c2−24b2+24ab+96b−6abc−16bc+9a2+24c−48a−56
x=2(a−b−c+3)−(3a−bc−4)−b2c2−24b2+24ab+96b−6abc−16bc+9a2+24c−48a−56:2(a−b−c+3)−3a+bc+4−b2c2−24b2+24ab+96b−6abc−16bc+9a2+24c−48a−56
2차 방정식의 해는 다음과 같다:x=2(a−b−c+3)−3a+bc+4+b2c2−24b2+24ab+96b−6abc−16bc+9a2+24c−48a−56,x=2(a−b−c+3)−3a+bc+4−b2c2−24b2+24ab+96b−6abc−16bc+9a2+24c−48a−56;a−b−c+3=0