Найдите произведение корней уравнения lg^2 х + lg x

Alenka2304 @Alenka2304

May 2022 1 29 Report

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

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БелкаАлександр

lg^2 х + lg x - 12 = 0

lg x=t

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

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