решите уравнения:[tex] \sqrt[3]{81x} + \sqrt[3]{243 x^{2} } = 6 [/tex][tex] \sqrt[5]{128 y^{2} } + \sqrt[5]{64y} = 24[/tex]. Created by ABC1234567. algebra-ru

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July 2022 1 6 Report

решите уравнения:
[tex] \sqrt[3]{81x} + \sqrt[3]{243 x^{2} } = 6 [/tex]

[tex] \sqrt[5]{128 y^{2} } + \sqrt[5]{64y} = 24[/tex]

Answers & Comments

Artem112

Verified answer

$\sqrt[3]{81x} + \sqrt[3]{243 x^{2} } = 6
\\\
3 \sqrt[3]{3x} + 3\sqrt[3]{9 x^{2} } = 6
\\\
\sqrt[3]{3x} =a
\\\
3a+3a^2+6
\\\
a^2+a-2=0
\\\
D=1+8=9
\\\
a_1=-2
\\
a_2=1
\\\
x= \frac{a^3}{3} 
\\\
x_1= \frac{-2^3}{3} = \frac{-8}{3} 
\\\
x_2= \frac{1^3}{3} = \frac{1}{3}$

$\sqrt[5]{128 y^{2} } + \sqrt[5]{64y} = 24
\\\
2 \sqrt[5]{4 y^{2} } +2 \sqrt[5]{2y} = 24
\\\
\sqrt[5]{2y} =a
\\\
2a^2+2a+24
\\\
a^2+a-12=0
\\\
D=1+48=49
\\\
a_1=-4
\\
a_2=3
\\\
x= \frac{a^3}{2} 
\\\
x_1= \frac{-4^5}{2} =-512
\\\
x_2= \frac{3^5}{2} =121.5$

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