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lenaaaaaaa85
@lenaaaaaaa85
July 2022
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Дробь : 1/3-lg x + 2/lg x -1=3
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scriptKIBBY
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).
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Answers & Comments
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).