已知x+y=3,xy=1.试求x^2+y^2,x-y,x^4+y^4的值

2025-01-02 10:48:12
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回答1:

(x+y)^2=9,x^2+y^2+2xy=9,x^2+y^2=9-2=7;
(x-Y)^2=x^2+y^2-2xy=7-2=5,x-y=正负根号5,
(x^2+y^2)^2=7^2,x^4+y^4+2x^2y^2=49,x^4+y^4=49-2=47