Question

√2х-1+(2х-1)=2 решите уравнение

Answer 1

$sqrt{2x-1}+2x-1=2 \ (sqrt{2x-1})^2=(2-2x+1)^2 \ 2x-1=(3-2x)^2 \ 2x-1=9-12x+4x^2 \ 2x-1-9+12-4x^2=0 \ 14x-10-4x^2=0\ 2x^2-7x+5=0 \ x_{1,2} = frac{-(-7)+-sqrt{(-7)^2-4*2*5}}{2*2} = frac{7+-3}{4} \ x_1 = 1 \ x_2= frac{5}{2}$