x³+y³=(x+y)(x²-xy+y²)=x²-xy+y²=(x+y)²-3xy=1-3xy=1/3∴xy=2/9x五次方+y五次方=(x³+y³)(x²+y²)-(x+y)x²y²=1/3*5/9-1*4/81=5/27-4/81=11/81
解:由x+y=1得y=1-x,代入x^3+y^3=1/3,打开化简得9x^2-9x+2=0,解得x=1/3或2/3,则y=2/3或1/3无论是哪一个,代入后答案都是11/81