Question

Извлечь корень
$sqrt{ (2x+1)^{2}-8x }$

Answer 1

$sqrt{(2x+1)^2-8x}\ sqrt{4x^2-4x+1}=\ sqrt{4(x^2-x+frac{1}{4})}=\ sqrt{4(x-frac{1}{2})^2}=|2(x-frac{1}{2})|=|2x-1|$
$|2x-1|\ x geq frac{1}{2}\ |2x-1|=2x-1\ \ x<frac{1}{2}\ 1-2x$