題目:求解 (x+1)(x二次方+1)(x三次方+1)=30*x三次方
作者:chpohoa1
顯然x=0不為其解
兩邊同除以x^3
=> [√x + 1/√x] * [x + 1/x] * [√(x^3) + 1/(√x^3)] = 30
令 √x + 1/√x = t
x + 1/x = t^2 - 2
√(x^3) + 1/(√x^3) = t^3 - 3t
=> t^2 * ( t^2 - 2 ) * (t^2-3) = 30
令 t^2 = u => (u^2 + 6)(u-5) = 0
=>x + 1/x = t^2 - 2 = -2 ± √6i ,3
=> x^2 + ( 2∓√6i) x + 1 = 0 , x^2 - 3x + 1 = 0
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