Question

решите уравнение 2-√x-1=x+1​

Answer 1

$2-\sqrt{x-1}=x+1\; ,\; \; \; ODZ:\; \; x-1\geq 0\; ,\; \; x\geq 1\\\\\sqrt{x-1}=1-x\; \; \Rightarrow \; \; 1-x\geq 0\; \; \to \; \; x\leq 1\\\\\left \{ {{x\geq 1} \atop {x\leq 1}} \right.\; \; \Rightarrow \; \; \; \underline {x=1}\\\\ili\\\\\sqrt{x-1}=1-x\; \; \to \; \; (x-1)=1-2x+x^2\\\\x^2-3x+1=0\; \; \to \; \; x_1=1\; ,\; \; x_2=2\; \; (teorema\; Vieta)\\\\Proverka\, :\; x=2\; \; \to \; \; 2-\sqrt1=2+1\; \; ,\; \; 1=3\; \; neverno\\\\x=1\, :\; 2-\sqrt0=1+1\; \; \to \; \; 2=2\; \; verno\\\\Otvet:\; \; x=1\; .$