Question

Sa se rezolve in R
log in baza 3 din (x+2)=log in baza 3 din x^2

Answer 1

[tex]log_{3}(x+2)=log_{3}x^2\\ x+2=x^2\\ x^2-x-2=0\\a=1\\b=-1\\c=-2\\ \Delta=b^2-4ac=(-1)^2-4*1*(-2)=1+8=9\\ x_1= \frac{-b- \sqrt{\Delta} }{2a}= \frac{1- \sqrt{9} }{2*1}= \frac{1-3}{2}= \frac{-2}{2}=-1\\ x_2= \frac{-b+ \sqrt{\Delta} }{2a}= \frac{1+\sqrt{9} }{2*1}= \frac{1+3}{2}= \frac{4}{2}=2\\ [/tex]
S={ - 1; 2}