lg²x^3-10lgx+1=0 решить уравнение. Created by 1357246078. algebra-ru

lg²x^3-10lgx+1=0 решить уравнение...

July 2022 1 9 Report

lg²x^3-10lgx+1=0 решить уравнение

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kirichekov Lg²x³=(lgx³)²=(3lgx)²=9(lgx)²
9(lgx)²-10lgx+1=0
обозначим lgx=t
9t²-10t+1=0
t₁=1/9, t₂=1
обратная замена
t₁=1/9 lgx=1/9, x=10¹/⁹
t₂=1 lgx=1, x=10¹
ответ: х₁=10¹/9, х₂=10

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