x+y=-3,x³+y³=-18,求x∧7+y∧7的值
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x+y=-3,x³+y³=-18,求x∧7+y∧7的值
x+y=-3,
(x+y)^3 = x^3 + y^3 + 3xy(x+y)
代入得:-27=-18-9xy xy=1
x^2 + y^2 = (x+y)^2 - 2xy = 9 - 2 =7
x^4 + y^4 = (x^2 + y^2)^2 - 2(xy)^2 = 49-2 =47
(x^3 + y^3)(x^4 + y^4)= x^7 + y^7 + x^3·y^3·(x+y)
-18*47 = x^7 + y^7 + (-3)
则X^7 + y^7 = -843
题真不简单呐,祝你好运哦~
(x+y)^3 = x^3 + y^3 + 3xy(x+y)
代入得:-27=-18-9xy xy=1
x^2 + y^2 = (x+y)^2 - 2xy = 9 - 2 =7
x^4 + y^4 = (x^2 + y^2)^2 - 2(xy)^2 = 49-2 =47
(x^3 + y^3)(x^4 + y^4)= x^7 + y^7 + x^3·y^3·(x+y)
-18*47 = x^7 + y^7 + (-3)
则X^7 + y^7 = -843
题真不简单呐,祝你好运哦~
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