Даю 50 баллов. Решите уравнения:
[tex]\sqrt{x\sqrt[5]{x}}-\sqrt[5]{x\sqrt{x}} = 56[/tex]
[tex]\sqrt{x\sqrt[5]{x}}-\sqrt[5]{x\sqrt{x}} = 56[/tex]
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√[x·x^(1/5)] - [x√x]^(1/5) = 56x^(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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Решение на фотографии.Надеюсь понятно.