Find the sum of the roots of the equation lg (5x-x2) = lg2 + lg3.

lg (5x – x ^ 2) = lg2 + lg3 – on the right side of the equation we apply the property of the sum of logarithms: The sum of logarithms with the same bases is equal to the logarithm of the product of expressions under the signs of the logarithms of the terms, logx a + logx b = logx (ab);

lg (5x – x ^ 2) = lg (2 * 3);

lg (5x – x ^ 2) = lg6 – if the bases of the logarithms are the same, then the expressions under the signs of the logarithms will be equal;

5x – x ^ 2 = 6;

x ^ 2 – 5x + 6 = 0;

D = b ^ 2 – 4ac;

D = (-5) ^ 2 – 4 * 1 ^ 6 = 25 – 24 = 1; √D = 1;

x = (-b ± √D) / (2a);

x1 = (5 + 1) / 2 = 6/2 = 3;

x2 = (5 – 1) / 2 = 4/2 = 2.

x1 + x2 = 3 + 2 = 5.

Answer. five.