已知(2x+2y+1)(2x+2y-1)=3 则x+y=___如题

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已知(2x+2y+1)(2x+2y-1)=3 则x+y=___如题

已知(2x+2y+1)(2x+2y-1)=3 则x+y=___如题
已知(2x+2y+1)(2x+2y-1)=3 则x+y=___
如题

已知(2x+2y+1)(2x+2y-1)=3 则x+y=___如题
2x+2y+1)(2x+2y-1)=3
(2x+2y)^2-1=3
(2x+2y)^2=4
4(x+y)^2=4
(x+y)^2=1
x+y=±1

(2x+2y+1)(2x+2y-1)
=4(x+y)^2 -1
=3
所以,(x+y)^2=1
x+y=±1

(2x+2y+1)(2x+2y-1)-3
=(2x+2y)^2-1-3
=(2x+2y)^2-2^2
=(2x+2y+2)(2x+2y-2)
=0
所以 2x+2y+2=0 或者 2x+2y-2=0
即 x+y=-1 或者 x+y=1

丨x 3丨 7(x 2y-1)的平方=0 x 3=0,x 2y-1=0 x=-3 y=(1-x)/2=2 2x-y=-6-2=-8

设z = x+y
(2z +1)(2z-1) = 3
4z^2 -1 = 3
z^2 = 1
z = 1, z = -1
x+y = 1或x+y = -1