Дробь : 1/3-lg x + 2/lg x -1=3

Question

Дробь : 1/3-lg x + 2/lg x -1=3

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Answer 1

1/(3 -  lgx) + 2/(lgx - 1) = 3;

(lgx -  1 + 6 -  2lgx)/((3 -  lgx)(lgx -  1)) = 3;

-lgx + 5 = 3(3 -  lgx) (lgx -  1);

-lgx + 5 = 9lgx -  9 -  3lg^2x + 3lgx;

-3lg^2x + 13lgx -  14 = 0;

lgx = a;

-3a^2 + 13a -  14 = 0;

D = 169 -  168 = 1;

a = - 2, a = 14/6 = 7/3;

lgx = -2 => 10^-2 = x, x = 1/100 = 0,01;

lgx = 7/3 => x = 10^(7/3). 

Ответ: 0,01; 10^(7/3).