k是整数,(k^2+2k-3)/(9-k^2)也是整数,求k的值
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![k是整数,(k^2+2k-3)/(9-k^2)也是整数,求k的值](/uploads/image/z/4374498-66-8.jpg?t=k%E6%98%AF%E6%95%B4%E6%95%B0%2C%28k%5E2%2B2k-3%29%2F%289-k%5E2%29%E4%B9%9F%E6%98%AF%E6%95%B4%E6%95%B0%2C%E6%B1%82k%E7%9A%84%E5%80%BC)
k是整数,(k^2+2k-3)/(9-k^2)也是整数,求k的值
k是整数,(k^2+2k-3)/(9-k^2)也是整数,求k的值
k是整数,(k^2+2k-3)/(9-k^2)也是整数,求k的值
原式=(k+3)(k-1)/[-(k+3)(k-3)]
=-(k-1)/(k-3)
=-[(k-3+2)/(k-3)]
=-1-2/(k-3)是整数
所以k-3=±1,±3
且分母9-k²≠0
所以k=2,k=4,k=0,k=6