some questions of F4 maths

2011-11-27 11:11 pm
solve the equation x^2/3 = 1/81 for x > 0

thank you very much!!!!!!!!!!!!!!!!!!!!!!

回答 (1)

2011-11-29 5:01 pm
✔ 最佳答案
x^2/3 = 1/81
x^2/3 = 1/(3^4)
Both sides take the cube first, then take the square root

(x^2/3)^(3/2) = [1/(3^4)]^(3/2)
x^[(2/3)*(3/2)] =1^(3/2)/(3^4)^(3/2) [note: (2/3)(3/2) = 1]
x^1 =1/(3^4)^(3/2)

1
x = -----------
3^4^(3/2)

1
x = ------------
3^(4*3/2)

1
x = -----------
3^(12/2)

1
x = -----------
3^6

x = 1/729

Note: * means multiply


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