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x+1/x=4 //·x
x²+1=4x
x²-4x+1=0
Δ=16-4=12
√Δ=2√3
x₁=(4-2√3)/2=2-√3
x₂=2+√3
dla x₂
x³+1/x³=(2+√3)³+1/(2+√3)³=8+12√3+18+3√3+1/(8+12√3+18+3√3)=26+15√3+
1/(26+15√3)=26+15√3+26-15√3=52
dlax₁
(2-√3)³+1/(2-√3)³=8-12√3+18-3√3+1/(8-12√3+18-3√3)=26-15√3+
1/(26-15√3)=26-15√3+26+15√3=52
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x+1/x=4 //·x
x²+1=4x
x²-4x+1=0
Δ=16-4=12
√Δ=2√3
x₁=(4-2√3)/2=2-√3
x₂=2+√3
dla x₂
x³+1/x³=(2+√3)³+1/(2+√3)³=8+12√3+18+3√3+1/(8+12√3+18+3√3)=26+15√3+
1/(26+15√3)=26+15√3+26-15√3=52
dlax₁
(2-√3)³+1/(2-√3)³=8-12√3+18-3√3+1/(8-12√3+18-3√3)=26-15√3+
1/(26-15√3)=26-15√3+26+15√3=52