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若x+y=3,xy=1,则x^5+y^5=

若x+y=3,xy=1,则x^5+y^5=

x+y=3,xy=1x²+y²=(x+y)²-2xy=9-2=7x³+y³=(x+y)薯晌³-3xy(x+y)=27-9=18所以x^5+y^5=(x²+y²)(x³+y³)-x²y³-x³y²=(x²+y²)(x³+y³氏手渣)-x²歼悄y²(x+y)=7×18-3=123