解方程:2(x2+1/x2)-9(x+1/x)+14=0(提示:令x+1/x=t)

题目

解方程:2(x2+1/x2)-9(x+1/x)+14=0(提示:令x+1/x=t)
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答案

令x+1/x=t
2(t²)-9(t)+10=0
(2t-5)(t-2)=0
解得 t=5/2或t=2
继续
x+1/x=5/2 → 2x²-5x+2=0 → (2x-1)(x-2)=0 → x=1/2或 x=2
x+1/x=2 → (x-1²)=0→ x=1