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由根與係數的關係可知:x1+x2=k+12,x1•x2=k+32.由已知兩根之差為1,得|x1-x2|=1,即(x1-x2)2=1.則(x1+x2)2-4x1x2=1.(k+1)24-2(k+3)=1,解得k=-3或9.故答案為:9或-3
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