Найдите наибольший корень уравнения ³√&oline;&oline;&oline;&oline;&oline;&oline;&oline;&oline;&oline; (9+8х²)/3 = 3. Created by Cuzya2929. algebra-ru

3 = 3...

Cuzya2929 @Cuzya2929

July 2022 2 2 Report

Найдите наибольший корень уравнения

³√‾‾‾‾‾‾‾‾‾
(9+8х²)/3 = 3

alex080297 (9+8x^2)/3=27
(9+8x^2)=81
8x^2=81-9
8x^2=72
x^2=9
x=+-3
Наибольший общий корень равен 3

1 votes Thanks 1

skvrttt $\mathtt{\sqrt[3]{\frac{8x^2+9}{3}}=3;~\frac{8x^2+9}{3}=27;~8x^2+9=81;~x=б\sqrt{\frac{81-9}{8}}=б\sqrt{9}=б3,~}\\\mathtt{x_{max}=3}$

$\mathtt{\frac{\sqrt[3]{8x^2+9}}{3}=3;~\sqrt[3]{8x^2+9}=9;~x=б\sqrt{\frac{9^3-9}{8}}=б\sqrt{\frac{9(81-1)}{8}}=б3\sqrt{10},~}\\\mathtt{x_{max}=3\sqrt{10}}$

2 votes Thanks 3

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