Question

решите уравнение: √x=2-x

Answer 1

$sqrt{x}=2-x; ,; ; ODZ:; ; left { {{x geq 0} atop {2-x geq 0}} right. ; left { {{x geq 0} atop {x leq 2}} right. ; to ; ; 0 leq x leq 2\\x=(2-x)^2\\x=4-4x+x^2\\x^2-5x+4=0\\x_1=1,; x_2=4; ; (teorema; Vieta)\\x_2=4notin [, 0,4, ]\\Proverka:; ; x=1; to ; ; sqrt1=2-1; ,; 1=1; verno\\Otvet:; x=1.$