tex]...

July 2022 1 12 Report

Помогите пожалуйста решить систему показательных уравнений:
[tex] \left \{ {{ 6^{x}+ y =2} \atop { 6^{2x} + 6^{x}=12 }} \right. [/tex]

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dtnth

Verified answer

Сделаем замену $6^x=t >0; 6^{2x}=(6^x)^2=t^2$

$6^{2x}+6^x=12$
$t^2+t-12=0$
$(t+4)(t-3)=0$
$t+4=0;t_1=-4$
$t-3=0;t_2=3$
$t=3$
$6^x=3;t=log_6 3$
$y=2-6^x=2-3=-1$
решение $(log_6 3;-1)$

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