若x눀=3y+8,y눀=-3x+8,且x+y≠0,则x대-y대值为

2025-06-26 11:00:42
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回答1:

x^2=3y+8 (1)
y^2=-3x+8 (2)

(1)-(2)
(x+y)(x-y) = 3(x+y)
(x+y)(x-y+3)=0
x-y = 3

(1)+(2)
x^2+y^2 = -3(x-y)+16
= -9+16
=7

(x-y)=3
(x-y)^2 =9
x^2-2xy +y^2 =9
7-2xy =9
xy = -1

x^3-y^3
=(x-y)(x^2+xy+y^2)
=3(x^2+xy+y^2)
=3( 7 -1)
=18