Question

Sa se rezolve in R a) log in baza 0,1 din (x^2-x-1)=log in baza 0,1 din (x+4) ofer 20 pncte

Answer 1

$log_{0,1}(x^2-x-1)=log_{0,1}(x+4)\\ x^2-x-1=x+4\\ x^2-x-1-x-4=0\\x^2-2x-5=0\\ a=1\\b=-2\\c=-5\\\Delta=b^2-4ac=(-2)^2-4*1*(-5)=4+20=24\\ \sqrt{24}= \sqrt{6*4}=2 \sqrt{6} \\ x_1= \frac{-b-\sqrt{\Delta}}{2a}= \frac{2- \sqrt{24} }{2*1}= \frac{2-2 \sqrt{6} }{2}= \frac{2(1- \sqrt{6} )}{2}=1- \sqrt{6}\\ x_2= \frac{-b+\sqrt{\Delta}}{2a}= \frac{2+ \sqrt{24} }{2*1}= \frac{2+2 \sqrt{6} }{2}= \frac{2(1+ \sqrt{6} )}{2}=1+ \sqrt{6} \\ S=[1- \sqrt{6}; 1+ \sqrt{6}]$

Solutia sa o scrii in acolade dar nu in paranteza patrata. In formula nu pot pune acoladele