早教吧作业答案频道 -->数学-->
已知（x+2）9=a0+a1x+a2x2+……+a9x9,则（a1+3a3+5a5+7a7+9a9)2-（2a2+4a4+6a6+8a8)2的值是?
题目详情
已知（x+2）9=a0+a1x+a2x2+……+a9x9,则（a1+3a3+5a5+7a7+9a9)2-（2a2+4a4+6a6+8a8)2的值是?
▼优质解答
答案和解析
(x+2)^9=a0+a1x+a2x^2+…+a9x^9
两边求导得
9(x+2)^8=a1+2a2x+3a3x^2…+9a9x^8
令x=1,
9(1+2)^8=a1+2a2+3a3…+9a9
9*3^8=a1+2a2+3a3…+9a9
3^2*3^8=a1+2a2+3a3…+9a9
3^10=a1+2a2+3a3…+9a9
a1+2a2+3a3…+9a9=3^10
令x=-1,
9(x+2)^8=a1+2a2x+3a3x^2…+9a9x^8
9(-1+2)^8=a1-2a2+3a3…+9a9
9*1^8=a1-2a2+3a3-4a4…+9a9
9=a1-2a2+3a3-4a4…+9a9
a1-2a2+3a3-4a4…+9a9=9
(a1+3a3+5a5+7a7+9a9)^2-(2a2+4a4+6a6+8a 8)^2
=[(a1+3a3+5a5+7a7+9a9)-(2a2+4a4+6a6+8a 8)][(a1+3a3+5a5+7a7+9a9)+(2a2+4a4+6a6+8a 8)]
=(a1+2a2+3a3…+9a9)(a1-2a2+3a3-4a4…+9a9)
=3^10*9
=3^10*3^2
=3^12
两边求导得
9(x+2)^8=a1+2a2x+3a3x^2…+9a9x^8
令x=1,
9(1+2)^8=a1+2a2+3a3…+9a9
9*3^8=a1+2a2+3a3…+9a9
3^2*3^8=a1+2a2+3a3…+9a9
3^10=a1+2a2+3a3…+9a9
a1+2a2+3a3…+9a9=3^10
令x=-1,
9(x+2)^8=a1+2a2x+3a3x^2…+9a9x^8
9(-1+2)^8=a1-2a2+3a3…+9a9
9*1^8=a1-2a2+3a3-4a4…+9a9
9=a1-2a2+3a3-4a4…+9a9
a1-2a2+3a3-4a4…+9a9=9
(a1+3a3+5a5+7a7+9a9)^2-(2a2+4a4+6a6+8a 8)^2
=[(a1+3a3+5a5+7a7+9a9)-(2a2+4a4+6a6+8a 8)][(a1+3a3+5a5+7a7+9a9)+(2a2+4a4+6a6+8a 8)]
=(a1+2a2+3a3…+9a9)(a1-2a2+3a3-4a4…+9a9)
=3^10*9
=3^10*3^2
=3^12
看了已知（x+2）9=a0+a1x...的网友还看了以下：
(-1又5分之2)2-(-0.1)3-丨-7分之2丨2-3（3）÷（-3）2-3分之1×（-3）3( 2020-03-31 …
S=(1+1/1*2+(2+1/2*3)+(3+1/3*4)+...+(20+1/20*21)S= 2020-04-27 …
根据3^2-1^2=8*1、5^3-3^2=8*2、7^2-5^2=8*3这个规律可得的结论是什么 2020-05-13 …
1、若｛An｝满足An=n2+λn (λ∈ N*）为递增数列,求实数λ的取值范围.2、已知数列｛A 2020-06-27 …
求1+2+2^2+2^3+2^4+…+2^2014的值.设S=1+2+2^2+2^3+2^4+…+ 2020-07-09 …
xyz=1,x+y+z=2,x^2+y^2+z^2=3,求x,y,z我解:xy=1/z,x+y=2- 2020-10-31 …
观察下列各式然后回答问题:1-1/2^2=1/2*2/3,1-1/3^2+2/3*4/3,1-1/4 2020-11-01 …
一次课堂练习，小明同学做了如下四道因式分解的题，你认为他做得不够完整的一题是（）A．2-2a2=2（ 2020-11-28 …
已知a,b属于正实数a^2+b^2/2=1求y=a√(1+b^2)的最大值参考书上是用y^2=[a√ 2020-12-31 …
这些题怎么数学解1已知(x+m)^2(x^2-2x+3)+x(x+1)中不含x^2项求m的值2已知a 2020-12-31 …