if (ax)^-1/2=b and b^2/3=a,express x in terms of a only.
答:x=1/a^4
f.3 maths指數定律
2007-07-31 10:14 am
回答 (2)
2007-07-31 10:30 am
✔ 最佳答案
( ax )^ - 1/2 = b ----- ( 1 )b ^ 2/3 = a --- ( 2 )
F o r m ( 1）：b ^ 2/3 = a
b^ ( 2/3 x 3/2 ) = a^ 3/2
b = a^ 3/2 ---- ( 3 )
P u t ( 3 ) i n t o ( 1 )
( ax )^ - 1/2 = a^ 3/2
x^ - 1/2 = ( a^ 3/2 ) / a ^ - 1/2 < a 的 指 數：3/2 - (-1/2) = 3/2 +1/2 = 2
x^ ( - 1/2 x -2 ) = a^ ( 2 x -2 )
x = a^ -4
x = 1/a^4
希望幫到你
參考: me
2007-07-31 10:40 am
(ax)^-1/2=b ------------------ (1)
b^2/3=a --------------------(2)
Sub (1) into (2):
[(ax)^ -1/2]^2/3=a
(ax) ^ -1/3 = a
(a ^ -1/3) (x ^ -1/3) = a
x ^ -1/3 = a / (a ^ -1/3)
x ^ -1/3 = a ^ 4/3
x = a ^ [(4/3) / (-1/3)]
x = a ^ -4 = 1 / (a^4)
b^2/3=a --------------------(2)
Sub (1) into (2):
[(ax)^ -1/2]^2/3=a
(ax) ^ -1/3 = a
(a ^ -1/3) (x ^ -1/3) = a
x ^ -1/3 = a / (a ^ -1/3)
x ^ -1/3 = a ^ 4/3
x = a ^ [(4/3) / (-1/3)]
x = a ^ -4 = 1 / (a^4)
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