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(x+1/x)²-3/2(x-1/x)=4
x²+1/x²+2-3/2(x-1/x)=4
x²+1/x²+2-4=3/2(x-1/x)
x²+1/x²-2=3/2(x-1/x)
(x-1/x)²=3/2(x-1/x)
x-1/x=3/2
2(x²-1)=3x
2x²-3x-2=0
2x²-4x+x-2=0
2x(x-2)+1(x-2)=0
(2x+1)(x-2)=0
2x+1=0, x-2=0
x=-1/2,2
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