Question

решить уравнения log12 x+log12(x+1)=1

Answer 1

log12(x) + log12(x+1) = 1
log12(x(x+1)) = 1
log12(x²+x) = log12(12¹)
log12(x²+x) = log12(12) => x²+x = 12
x²+x-12 = 0
По теореме обратной теореме Виета:
х1 + х2 = -1 и х1 × х2 = -12 => х1 = -4; х2 = 3
Ответ: -4; 3