已知a=3a^2-3/2a+3b^2-3c^2,b=2a^2+b+2b^2-c^2.且a与b互为相反数.|c|=2,若2a-3b+c=0,求c的值

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a与b互为相反数,则a+b=0,a= -b
a=3a^2-3/2a+3b^2-3c^2,3c^2=3a^2-5/2a+3b^2 = 5/2b+6b^2
b=2a^2+b+2b^2-c^2,3c^2=6a^2+6b^2= 12b^2
5/2b+6b^2= 12b^2即：12b^2-5b=0；b=0或5/12
若2a-3b+c=0,则：-2b-3b+c=0,-5b+c=0,c = 5b = 0 或 25/12；
|c|=2,c=±2