Question

решите уравнение arccos(2x^2-1)=arccoc(3x+1)

Answer 1

ОДЗ:
$left { {{-1 leq 2x^2-1 leq 1} atop {-1 leq 3x+1 leq 1}} right. textless = textgreater left {{{0 leq 2x^2 leq 2 } atop {-2 leq 3x leq 0}} right. textless = textgreater left { {{0 leq x^2 leq 1} atop {- frac{2}{3} leq x leq 0 }} right. textless = textgreater left { {{ x^2 leq 1} atop {- frac{2}{3} leq x leq 0 }} right. \ \ left { {{-1 leq x leq 1} atop {- frac{2}{3} leq x leq 0 }} right. textless = textgreater -frac{2}{3} leq x leq 0$



$arccos(2x^2-1)=arccos(3x+1) \ \ 2x^2-1=3x+1 \ \ 2x^2-3x-2=0 \ \ D=9+4*2*2=9+16=25=5^2 \ \ x_1= frac{3-5}{2*2}= -frac{1}{2}$
$x_2= frac{3+5}{2*2} =2$  -  не удовлетворяет ОДЗ.

Ответ: -1/2