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log32乘以[根号（2+根号三）-根号（2-根号三）] 32是底数

分类: 作业答案 • 2022-02-19 14:10:10
问题描述：

log32乘以[根号（2+根号三）-根号（2-根号三）] 32是底数

答

[3^(1/2) + 1]^2 = 4 + 2(3)^(1/2),
2 + 3^(1/2) = [3^(1/2) + 1]^2/2,
[2 + 3^(1/2)]^(1/2) = [3^(1/2) + 1]/2^(1/2).
[3^(1/2) - 1]^2 = 4 - 2(3)^(1/2),
2 - 3^(1/2) = [3^(1/2) - 1]^2/2,
[2 - 3^(1/2)]^(1/2) = [3^(1/2) - 1]/2^(1/2).
[2 + 3^(1/2)]^(1/2) - [2 - 3^(1/2)]^(1/2)
= [3^(1/2) + 1]/2^(1/2) - [3^(1/2) - 1]/2^(1/2)
= 2/2^(1/2)
= 2^(1/2)
log_{32}{[2 + 3^(1/2)]^(1/2) - [2 - 3^(1/2)]^(1/2)}
= ln{2^(1/2)}/ln(32)
= [ln(2)/2]/[5ln(2)]
= 1/10

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