Даю 50 баллов. Решите уравнения: [tex]\sqrt{x\sqrt[5]{x}}-\sqrt[5]{x\sqrt{x}} = 56[/tex]. Created by barenzi. algebra-ru

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August 2022 2 15 Report

Даю 50 баллов. Решите уравнения:

[tex]\sqrt{x\sqrt[5]{x}}-\sqrt[5]{x\sqrt{x}} = 56[/tex]

Verified answer

√[x·x^(1/5)] - [x√x]^(1/5) = 56

x^(3/5) - x^(3/10) = 56

t = x^(3/10) > 0

t² - t - 56 = 0

t = -7 (посторонний корень)
t = 8

x^(3/10) = 8

x³ = 8^10

x = 8^(10/3) = 2^10 = 1024

Ответ: 1024

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