方法多:1)可這樣做,據(jù)條件,a,2a為其根代入18*a^3+9*a^2-74*a+40 = 0,144*a^3+36*a^2-148*a+40 = 0,消去3,2次項(xiàng)即得;{x1=a = 2/3},{x2=2a= 4/3},{x3 = -5/2};
2)4個(gè)根有2個(gè)重根a,2個(gè)重根b,說(shuō)明:原方程是一個(gè)平方式;可設(shè)為(x^2+p*x+q)^2=x^4+4x^3+10x^2+12x+9,則有2p=4;q^2=9;2pq=12,所以p=2,q=3;所以有:
x^2+2*x+3=0,所以a=-1+sqrt(2)*I,b=-1-sqrt(2)*I;或者a=-1-sqrt(2)*I,b=-1+sqrt(2)*I.