感謝你對中學生數(shù)理化團隊的信任1
4題都完成了,
1
(1-1/2^2)(1-1/3^2)(1-1/4^2)...(1-1/2001^2)(1-1/2002^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4).(1-1/2002)(1+1/2002)
=1/2*3/2*2/3*4/3*3/4*5/4*.*2001/2002*2003/2002
=1/2*2003/2002
=2003/2004
2
[（4^9+16^4)*3^2]/[(2^17+2^15)*2^7]
=[(2^18+2^16)*3^2]/(2^2+1)*2^15*2^7]
=[(2^2+1)*2^16*3^2]/(2^2+1)*2^16*2^6]
=3^2/2^6
=9/64
3
a^(n+2)-6a^n+5a^(n-1)
=a^(n-1)[a^3-6a^2+5]
=a^(n-1)[a^3-a^2-5(a^2-1)]
=a^(n-1)[a^2(a-1)-5(a-1)(a+1)]
=a^(n-1)*(a-1)*(a^2-5a-5)
=a^(n-1)*(a-1)*[a-(5-3√5)/5]*[a-(5+3√5)/5]
4
2x^2-5xy+2y^2+4x-5y+k
參照前三項,若能分解,那么只能分解成
(2x-y+a)(x-2y+b) 的形式
展開 (2x-y+a)(x-2y+b)
=2x²-5xy+2y²+(a+2b)x-(b+2a)y+ab
與原式比對：
a+2b=4,2a+b=5,ab=k
解得a=2,b=1,k=2
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