Question

Найдите произведение корней уравнения
lg^2 х + lg x - 12 = 0

Answer 1

lg^2 х + lg x - 12 = 0

lg x=t

$t^{2} + t-12=0\D=1-4*1*(-12)=49\t_{1} =frac{-1+sqrt{49} }{2*1} =3\t_{2} =frac{-1-sqrt{49} }{2*1} =-4\lg x_{1}=3\lg x_{2}=-4\x_{1}=1000\x_{2}=frac{1}{10000} \\1000*frac{1}{10000}=frac{1}{10}$