Question

lg($x^{2} -20x + 75$) = lg(x-5) + 2
решите неравенство

Answer 1

$lg(x^2-20x+75)=lg(x-5)+2\lg(x^2-20x+75)=lg(x-5)+lg100\lg(x^2-20x+75)=lg(x-5)+2\lg(x^2-20x+75)=lg(100x-500)\x^2-20x+75=100x-500\x^2-120x+575=0\x_{1,2}=60^+_-sqrt{3600-575}\x_1=115 ;x_2=5$