помогите решить12^x-6^(x-1)+8*3^x=0. Created by livine08. algebra-ru

Ответ в приложении........

помогите решить12^x-6^(x-1)+8*3^x=0...

uekmyfhfp 12^x - 6^x * 6 + 8* 3^x = 0; /:6^x ;
(12^x / 6^x) - 6*(6^x/6^x) + 8*(3^x / 6^x) =0;
2^x - 6 + 8 *(1/2)^x = 0;
2^x - 6+ 8 / 2^x = 0;
2^x = t; t > 0;
t - 6 + 8 / t = 0;
t^2 - 6 t + 8 = 0;
D = 4 = 2^2;
t1 = (6+2) /2= 4; ⇒ 2^x = 4; 2^x = 2^2; x = 2;
t2= ( 6-2) / 2 = 2; ⇒ 2^x = 2 ; 2^x = 2^1 ; x = 1.
Ответ х = 1 или х = 2

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