设x1 x2是方程2x^2-6x+3=0的两个根,求x1^3+x2^3
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![设x1 x2是方程2x^2-6x+3=0的两个根,求x1^3+x2^3](/uploads/image/z/3136207-31-7.jpg?t=%E8%AE%BEx1+x2%E6%98%AF%E6%96%B9%E7%A8%8B2x%5E2-6x%2B3%3D0%E7%9A%84%E4%B8%A4%E4%B8%AA%E6%A0%B9%2C%E6%B1%82x1%5E3%2Bx2%5E3)
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设x1 x2是方程2x^2-6x+3=0的两个根,求x1^3+x2^3
设x1 x2是方程2x^2-6x+3=0的两个根,求x1^3+x2^3
设x1 x2是方程2x^2-6x+3=0的两个根,求x1^3+x2^3
x1 x2是方程2x^2-6x+3=0的两个根,
∴x1+x2=-6÷(-2)=3
x1x2=3/2
x1^3+x2^3
=(x1+x2)(x1²-x1x2+x2²)
=(x1+x2)[(x1²+2x1x2+x2²)-3x1x2]
=(x1+x2)[(x1+x2)²-3x1x2]
=3×(3²-3×3/2)
=27/2