標題:
數學-指數,根式唔識help!!急~.
18,19,20,22,23,28,29,34 圖片參考：http://imgcld.yimg.com/8/n/HA00712931/o/701111180065913873402996.jpg 更新: 死圖請告知
最佳解答:
18) √(a)b / (a√b)^(-3/2) = a^(1/2) * b * a^(-1 * -3/2) * b^(-1/2 * -3/2) = a^(1/2) * b * a^(3/2) * b^(3/4) = a^(1/2 + 3/2) * b^(1 + 3/4) = a^2b^(7/4) 19) (a/b)^(3/2) * (b/a)^(1/2) / (a/b)^(-3/6) = a^(3/2) * b^(-3/2) * b^(1/2) * a^(-1/2) * a^(3/6) * b^(-3/6) = a^(3/2 - 1/2 + 1/2) * b^(-3/2 + 1/2 - 1/2) = a^(3/2)b^(-3/2) = a^(3/2)/b^(3/2) 20) x√(y^3) / √(x√y) = x * y^(3/2) * x^(-1/2) * y^(-1/4) = x^(1 - 1/2) * y^(3/2 - 1/4) = x^(1/2)y^(5/4) 22) 16^(k - 1) / (^4√(256^(k - 2)) * 8^(-k)) = 2^(4k - 4) / (2^(2k - 4) * 2^(-3k)) = 2^(4k - 4) * 2^(-2k + 4) * 2^(3k) = 2^(4k - 4 - 2k + 4 + 3k) = 2^(5k) = 32^k 23) (a^(1/3) - 1)(a^(2/3) + a^(1/3) - 1) = a^(1/3) * (a^(2/3) + a^(1/3) - 1) - (a^(2/3) + a^(1/3) - 1) = a + a^(2/3) - a^(1/3) - a^(2/3) - a^(1/3) + 1 = a - 2a^(1/3) + 1 28) (√63 - √3)(3√7 - √12) = (3√7 - √3)(3√7 - 2√3) = 9(7) - 3√21 - 6√21 + 2(3) = 63 + 6 - 9√21 = 69 - 9√21 29) (4√5 + √3)(√5 - 4√3) = 4(5) + √15 - 16√15 - 4(3) = 20 - 12 - 15√15 = 8 - 15√15 34) a. (1 + √2 + √3)(1 + √2 - √3) = ((1 + √2) + √3)((1 + √2) - √3) = (1 + √2)^2 - (√3)^2 = 1 + 2√2 + 2 - 3 = 2√2 b. 1/(1 + √2 + √3) = 1/(1 + √2 + √3) * (1 + √2 - √3)/(1 + √2 - √3) = (1 + √2 - √3)/(2√2) = (2 + √2 - √6)/4
其他解答:
數學-指數,根式唔識help!!急~.
此文章來自奇摩知識+如有不便請留言告知
發問:18,19,20,22,23,28,29,34 圖片參考：http://imgcld.yimg.com/8/n/HA00712931/o/701111180065913873402996.jpg 更新: 死圖請告知
最佳解答:
18) √(a)b / (a√b)^(-3/2) = a^(1/2) * b * a^(-1 * -3/2) * b^(-1/2 * -3/2) = a^(1/2) * b * a^(3/2) * b^(3/4) = a^(1/2 + 3/2) * b^(1 + 3/4) = a^2b^(7/4) 19) (a/b)^(3/2) * (b/a)^(1/2) / (a/b)^(-3/6) = a^(3/2) * b^(-3/2) * b^(1/2) * a^(-1/2) * a^(3/6) * b^(-3/6) = a^(3/2 - 1/2 + 1/2) * b^(-3/2 + 1/2 - 1/2) = a^(3/2)b^(-3/2) = a^(3/2)/b^(3/2) 20) x√(y^3) / √(x√y) = x * y^(3/2) * x^(-1/2) * y^(-1/4) = x^(1 - 1/2) * y^(3/2 - 1/4) = x^(1/2)y^(5/4) 22) 16^(k - 1) / (^4√(256^(k - 2)) * 8^(-k)) = 2^(4k - 4) / (2^(2k - 4) * 2^(-3k)) = 2^(4k - 4) * 2^(-2k + 4) * 2^(3k) = 2^(4k - 4 - 2k + 4 + 3k) = 2^(5k) = 32^k 23) (a^(1/3) - 1)(a^(2/3) + a^(1/3) - 1) = a^(1/3) * (a^(2/3) + a^(1/3) - 1) - (a^(2/3) + a^(1/3) - 1) = a + a^(2/3) - a^(1/3) - a^(2/3) - a^(1/3) + 1 = a - 2a^(1/3) + 1 28) (√63 - √3)(3√7 - √12) = (3√7 - √3)(3√7 - 2√3) = 9(7) - 3√21 - 6√21 + 2(3) = 63 + 6 - 9√21 = 69 - 9√21 29) (4√5 + √3)(√5 - 4√3) = 4(5) + √15 - 16√15 - 4(3) = 20 - 12 - 15√15 = 8 - 15√15 34) a. (1 + √2 + √3)(1 + √2 - √3) = ((1 + √2) + √3)((1 + √2) - √3) = (1 + √2)^2 - (√3)^2 = 1 + 2√2 + 2 - 3 = 2√2 b. 1/(1 + √2 + √3) = 1/(1 + √2 + √3) * (1 + √2 - √3)/(1 + √2 - √3) = (1 + √2 - √3)/(2√2) = (2 + √2 - √6)/4
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