Question

Объясните пожалуйста

Answer 1

$sqrt{x+2sqrt{x-1}}+sqrt{x-2sqrt{x-1}} =\\=sqrt{(1+sqrt{x-1})^2}+sqrt{(1-sqrt{x-1})^2} =\\=|1+sqrt{x-1}|+|1-sqrt{x-1}|=\\=1+sqrt{x-1}+|1-sqrt{x-1}|=A\\a); ; ; esli; ; (1-sqrt{x-1})geq 0; ,; to; ; |1-sqrt{x-1}|=1-sqrt{x-1},; togda\\A=1+sqrt{x-1}+1-sqrt{x-1}=2; ;\\star ; 1-sqrt{x-1}geq 0; ,; ; sqrt{x-1}leq 1; ,; ; x-1leq 1; ,; xleq 2\\star ; ; x-1geq 0; ,; ; xgeq 1\\underline {1leq xleq 2}\\b); ; esli; ; (1-sqrt{x-1}) textless 0; ,; to; ; |1-sqrt{x-1}|=sqrt{x-1}-1.; togda\\A=1+sqrt{x-1}+sqrt{x-1}-1=2sqrt{x-1}; .$

$star ; ; 1-sqrt{x-1} textless 0; ,; ; sqrt{x-1} textgreater 1; ,; ; x-1 textgreater 1; ,; ; underline {x textgreater 2}\\c); ; A= left { {{2; ,; esli; ; 1 leq x leq 2} atop {2sqrt{x-1}; ,; esli; ; x textgreater 2}} right.$