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

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

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

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