Question

Решите уравнение:
$sqrt{9-4x|x-4|} -4x = 3$

Answer 1

$sqrt{9-4x|x-4|}-4x=3, \ sqrt{9-4x|x-4|}=4x+3, \ 4x+3 geq 0, x geq -0,75; \ 9-4x|x-4|=(4x+3)^2, \ 9-4x|x-4|=16x^2+24x+9, \ -4x|x-4|=16x^2+24x, \ x|x-4|=-4x^2-6x, \ 1) x=0, \ 0cdot|0-4|=-4cdot0-6cdot0, \ 0=0, \ x_1=0; \ 2) x neq 0, \ |x-4|=-4x-6, \-4x-6 geq 0, 2x+3 leq 0, x leq -1,5; \ xinvarnothing. \ x=0.$