Question

有一道高二文科数学题不会,请大家详细解释一下,谢谢

x,y∈R,x/(1-i) -y/(1-2i)=5/(1-3i)则xy=( )

Answer 1

x/(1-i) -y/(1-2i)=5/(1-3i)
x/2 (1+i)-y/5 (1+2i)=1/2 (1+3i)
(x/2-y/5)+(x/2 -2y/5)i=1/2 +3/2 i
∴x/2-y/5=1/2 且x/2 -2y/5=3/2，解得x=-1,y=-5,于是xy=5

Answer 2

分子父母有理化后求解，先去分母，然后根据实部，虚部对应相等，求解
解得x=-1,y=-5,则xy=5