Question

方程2(x²+1/x²)-3(x+1/x)=1的实数根是多少?

Answer 1

令a=x+1/x

则a²=x²+2+1/x²

所以即2(a²-2)-3a=1

2a²-3a-5=0

(2a-5)(a+1)=0

a=5/2,a=-1

x+1/x=5/2

2x²-5x+2=0

(2x-1)(x-2)=0

x=1/2,x=2

x+1/x=-1

x²+x+1=0

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