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求式中x的值,64(x-2)³-1=0.
解:(x-2)³=1/64;
∴ x=2+(1/4)[cos(2kπ/3+isin(2kπ/3)]
k=0时得 x₁=2+1/4=9/4;
k=1时得 x₂=2+(1/4)(-1/2+i√3/2)=15/8+i√3/8;
k=2时得 x₃=2+(1/4)(-1/2-i√3/2)=15/8-i√3/8;
解:(x-2)³=1/64;
∴ x=2+(1/4)[cos(2kπ/3+isin(2kπ/3)]
k=0时得 x₁=2+1/4=9/4;
k=1时得 x₂=2+(1/4)(-1/2+i√3/2)=15/8+i√3/8;
k=2时得 x₃=2+(1/4)(-1/2-i√3/2)=15/8-i√3/8;
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