Question

Помогите решить тринадцатый номер, пожалуйста!

Answer 1

$sqrt{(4cos3x-5)^2}-sqrt{cos^23x-8cos3x+16}=4\\sqrt{(4cos3x-5)^2}-sqrt{(cos3x-4)^2}=4\\|4cos3x-5|-|cos3x-4|=4\\t=cos3x,; ; |4t-5|-|t-4|=4\\4t-5=0; to ; t=frac{5}{4}=1,25\\t-4=0; to ; t=4\\Znaki; (4t-5):; ; ---(frac{5}{4})+++(4)+++\\Znaki; (t-4):; ; ---(frac{5}{4})---(4)+++$

$1); t leq frac{5}{4}; ; to ; |4t-5|=-(4t-5)=5-4t,; ; |t-4|=-(t-4)=4-t\\5-4t-(4-t)=4; ,; ; -3t=3,; ; t=-1\\cos3x=-1; ,; ; 3x=pi +2pi n,; ; ; x=frac{pi}{3}+frac{2pi n}{3},; nin Z\\2); ; frac{5}{4} textless t leq 4; ; to ; |4t-5|=4t-5,; ; |t-4|=-(t-4)=4-t\\4t-5-(4-t)=4; ,; ; 5t=13; ,; ; t=frac{13}{5} textgreater 1; to \\cos3x=frac{13}{5}; ; ne; imeet; reshenij\\3); ; t textgreater 4; to ; |4t-5|=4t-5; ,; ; |t-4|=t-4\\4t-5-(t-4)=4; ,; ; 3t=5,$

$t=frac{5}{3}notin (4,+infty )$

Oтвет: $x=frac{pi}{3}+frac{2pi}{3}n,nin Z$