解方程2（x^2+1/x^2)-3(x+1/x)=1

Question

解方程2（x^2+1/x^2)-3(x+1/x)=1

Answer 1

令x+1/x=t
x²+1/x²=t²-2
2（x^2+1/x^2)-3(x+1/x)=1
2(t²-2)-3t=1
2t²-4-3t-1=0
2t²-3t-5=0
(2t+2)(t-5/2)=0
t=-1 舍去 ∵x²+1/x²≥0 ∴t²-2≥0
t=5/2
当t=5/2时 x+1/x=5/2 解得x=2 或x=-1/2
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