Вычислить 1)8^3/2 /32^3/2 2)5*4^3/2-(4^0.5)^3 Найти значение выражения 2v3cos^2 17п/12-2v3 sin^2 17п/12

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1) 8^(3/2) / 32^(3/2)
8^(3/2) = (2^3)^(3/2) = 2^9/2 = 2^4.5 = sqrt(2^9) = sqrt(512) = 8sqrt(2)
32^(3/2) = (2^5)^(3/2) = 2^7.5 = sqrt(2^15) = sqrt(32768) = 8sqrt(512)

(8sqrt(2)) / (8sqrt(512)) = sqrt(2) / sqrt(512) = sqrt(2 / 512) = sqrt(1 / 256) = 1 / 16

2) 54^(3/2) - (4^0.5)^3
4^(3/2) = 44^(1/2) = 4*2 = 8
(4^0.5)^3 = 2^3 = 8

5*8 - 8 = 40 - 8 = 32

3) 2sqrt(3)cos^2(17π/12) - 2sqrt(3)sin^2(17π/12)
cos(17π/12) = -cos(π/12) = -cos(15π/12) = -cos(π - π/12) = -cos(π)cos(π/12) + sin(π)sin(π/12) = -cos(π/12)
= -cos(π/3) = -1/2
sin(17π/12) = -sin(π/12) = -sin(-π/12) = sin(π/12) = sin(π/3) = 1/2

2sqrt(3)(-1/2)^2 - 2sqrt(3)(1/2)^2 = 2sqrt(3)1/4 - 2sqrt(3)1/4 = (1/2)sqrt(3) - (1/2)sqrt(3) = 0

Ответ: 0