Question

一元三次方！(1＋q)∧3/(q＋q∧2)＝3/2 过程！

Answer 1

(1+q)^3/(q+q^2)
=(1+q)^3/[q(1+q)]
=(1+q)^2/q=3/2

(1+q)^2=(3/2)q
1+2q+q^2=(3/2)q
q^2+(1/2)q+1=0
q^2+(1/2)q+(1/16)=-15/16
(q+1/4)^2=-15/16
q+1/4=±(√15/4)i
q=(-1±√15i)/4

Answer 2

(1＋q)^3/(q＋q^2)＝3/2
2(1+3q+3q^2+q^3)=3(q+q^2)
2q^3+3q^2+3q+2=0
let
f(q)=2q^3+3q^2+3q+2
f(-1)=0
let
f(q) =(q+1)(2q^2+q+2)
q=-1 ( no real roots for 2q^2+q+2=0 )