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(急!证明对于任意自然数n,3^(n+2) - 2^(n+3)+3^n-2^(n+1)一定能被10整除.
(1)证明对于任意自然数n,3^(n+2) - 2^(n+3) + 3^n - 2^(n+1)一定能被10整除.
(2)若a-b=2,a-c=0.5,求(b-c)^2 - 3(b-c)+9/4的值.
(3)已知6x^2-5xy+y^2+mx+ny+2=(3x-y-2)(2x-y-1).求证:m=-7,n=3.
人气:220 ℃ 时间:2019-11-23 08:23:37
解答
3^(n+2) - 2^(n+3) + 3^n - 2^(n+1)
=(3^2*3^n+3^n)-(2^3*2^n+2*2^n)
=3^n(3^2+1)-2^n(2^3+2)
=10*3^n-10*2^n
=10*(3^n-2^n)
所以一定能被10整除
a-b=2,a-c=0.5
相减
(a-b)-(a-c)=2-0.5
c-b=1.5
b-c=-1.5
(b-c)^2 - 3(b-c)+9/4
=2.25+4.5+2.25
=9
(3x-y-2)(2x-y-1).
=6x^2-3xy-3x-2xy+y^2+y-4x+2y+2
=6x^2-5xy+y^2-7x+3y+2
=6x^2-5xy+y^2+mx+ny+2
对应项系数相等
所以m=-7,n=3
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