maths F5－rll33xb99t的部落格

標題:

maths F4

發問:

﹒。．☆....﹒。．∴＊?．﹒..∴☆．.﹒.∴﹒． 1 4^n x 3^2n-1/36^n+1 2 [ X m X m Xm Xm....Xm/m+m+m.....+m]2M times 3ｙ不等如０２ｙ^a-b x 3y^b-c x 4y^c-a 4 If 2(9^m/2) =a^3 a>1 27^m=? 5 If 4^a+2 =144 4^-a/2 =? 更新: 得1題岩左??1) 4n次方 x 3 2n-1次方 /36 n+1次方 =? 2) simplify [mxmxmx.......xm/m+m+m+......+m] 3) y不等於 0 2y a-b次方 x 3 y b-c次方 x 4y c-a次方 4) if 4a+2 次方 =144 then 4 -a/2次方 =? 更新 2: 2) simplify [mxmxmx.......xm/m+m+m+......+m] 呢題冇人識?? ans 1/2 m^m 1/2m 1/2m^2(m-1) 1/4 m^2m-1 更新 3: simplify [mxmxmx.......xm/m+m+m+......+m] 2m times

最佳解答:

1. {(4^n)[3^(2n-1)]} / [36^(n+1)] = {(4^n)[3^(-1)][3^(2n)]} / [(36)(36^n)] = [(4^n)[3^(-1)](9^n)] / [(36)(36^n)] = {[3^(-1)](36^n)} / [(36)(36^n)] = [3^(-1)] / (36) = 1 / 108 2. (m x m x m x ....... x m) / (m + m + m + ...... + m) = (m^m) / (m^2) = m^(m – 2) 3. 2 [y^(a-b)] x 3 [y^(b-c)] x 4 [y^(c-a)] = 24 [y^(a-b+b-c+c-a)] = 24 y^0 = 24 4. 2[9^(m/2)] = a^3 2(3^m) = a^3 3^m = (a^3)/2 (3^m)^3 = [ (a^3)/2 ]^3 3^(3m) = (a^9)/8 27^m = (a^9)/8 5. 4^(a+2) = 144 (4^a)(4^2) = 144 4^a = 144/(4^2) 4^a = 9 4^(-a/2) = 9^(-1/2) 4^(-a/2) = 1/3 有錯請指正! 有問題歡迎提出! 2007-12-23 15:23:50 補充：你第2題的問題是甚麼?請問是不是:[m x m x m x ....... x m / m + m + m + ...... + m] 的 (2m) 次方?假設是, 答案是:[m x m x m x ....... x m / m + m + m + ...... + m] ^(2m)= [(m^m)/(m^2)]^(2m)= [m^(m-2)]^(2m)= m^(2m^2 - 4m)請檢查清楚問題, 謝謝! 2007-12-25 21:40:15 補充：我似乎明你的問題是甚麼了.[(m x m x m x ....... x m) / (m + m + m + ...... + m)] 上下分別有 2m 次.(m x m x m x ....... x m)
其他解答:

1) 4^n x 3^2n-1/36^n+1 =2^2n*3^2n-(1/6)^2n+1^2n =6^2n-6^(-1)(2n)+1^2n =6^2n-6^-2n+1^2n (不是*不能約) 2) (XmXmXmXm....Xm/m+m+m.....+m)2M times =(X^2M) (m^2M)/ (m*2M) (都係不能約= =) 3)ｙ不等如０２ｙ^a-b x 3y^b-c x 4y^c-a 你想問２ｙ^a-b x 3y^b-c x 4y^c-a 定係２ｙ^(a-b) x 3y^(b-c) x 4y^(c-a)=.=? 前者係24y^(a+b+c)-8cy^(a+c)-12by^(a+c)+4bcy^c-6ay^(a+b)+2acy^a+3aby^b-bc 設２ｙ^(a-b) x 3y^(b-c) x 4y^(c-a)=O 12y^(a-b) x 12y^(b-c) x 12y^(c-a)=6*4*3 O 12y^0=72 O 12=72 O O=1/6 4)2(9^m/2) =a^3 2(3^m)=a^3 3^m=(a^3)/2 (3^m)^3=[ (a^3)/2 ]^3 3^3m=(a^9)/8 27^m =(3^3)^m =3^3m =(a^9)/8 5)4^a+2 =144 4^a=142 4^-a=1/142 4^-a/2= 為開方根