10*x^(1/6)-3*x^(1/3)-3=0. Created by igvolume11. algebra-ru

Пусть , тогда , при этом t ≥ 0.Ответ:

3)-3=0...

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August 2022 1 9 Report

10*x^(1/6)-3*x^(1/3)-3=0

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Пусть $x^{\frac{1}{6}}=t$ , тогда $x^{\frac{1}{3}}=(x^{\frac{1}{6}})^2=t^2$ , при этом t ≥ 0.

$10t-3t^2-3=0\\3t^2-10t+3=0\\D_{/4}=25-3*3=16=4^2\\t_{1}=\frac{5-4}{3}=\frac{1}{3}; t_{2}=\frac{5+4}{3}=3\\x^{\frac{1}{6}}=\frac{1}{3}; x^{\frac{1}{6}}=3\\x=\frac{1}{729}; 729$

Ответ: $\frac{1}{729}; 729$

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