作业帮x+y=2,x^3+y^3=14,求x^4+y^4,x^7+y^7
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/16 02:15:58
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x+y=2,x^3+y^3=14,求x^4+y^4,x^7+y^7
x+y=2,x^3+y^3=14,求x^4+y^4,x^7+y^7
x+y=2,x^3+y^3=14,求x^4+y^4,x^7+y^7
7=14÷2=(x³+y³)÷(x+y)=x²-xy+y²=(x+y)²-3xy
又因为x+y=2,
所以xy=-1,x²+y²=6
所以,x⁴+y⁴=(x²+y²)²-2x²y²=6²-2×(-1)²=34
x^7+y^7=(x⁴+y⁴)(x³+y³)-x³y³(x+y)=34×14-(-1)³×2=478
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