作业帮(n+1)(n+2)(n-4)(n-5)+k为完全平方式,求K的值急
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(n+1)(n+2)(n-4)(n-5)+k为完全平方式,求K的值急
(n+1)(n+2)(n-4)(n-5)+k为完全平方式,求K的值
急
(n+1)(n+2)(n-4)(n-5)+k为完全平方式,求K的值急
(n+1)(n+2)(n-4)(n-5)+k
=[(n+1)(n-4)][(n+2)(n-5)]+k
=(n^2-3n-4)(n^2-3n-10)+k
=(n^2-3n)^2-14(n^2-3n)+40+k
因为(n+1)(n+2)(n-4)(n-5)+k为完全平方式
所以40+k=49,k=9
所以(n+1)(n+2)(n-4)(n-5)+k=(n^2-3n-7)^2
(n+1)(n+2)(n-4)(n-5)+k
=(n+1)(n-4)(n+2)(n-5)+k
=(n²-3n-4)(n²-3n-10)+k
=(n²-3n-4)²-6(n²-3n+4)+k
因为是完全平方数，k=9
(n+1)(n+2)(n-4)(n-5)+k
=(n+1)(n-4)(n+2)(n-5)+k
=(n^2-3n-4)(n^2-3n-10)+k
=(n^2-3n)^2-4(n^2-3n-10)+k
=(n^2-3n)^2-4(n^2-3n)+40+k
=(n^2-3n)^2-4(n^2-3n)+4+36+k
=[(n^2-3n)-2]^2+36+k
即36+k=0
k=-36
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