Question

Sa se rezolve in Z ecuatiile a) | x-1. | =4. b) | x. + 5 | = - 2​

Answer 1

 

$\displaystyle\bf\\a)\\|x-1|=4\\\\x-1=\pm4\\\\Ecuatia~1:\\x-1=4\\x=4+1\\\boxed{\bf~x_1=5}\\\\Ecuatia~2:\\x-1=-4\\x=-4+1\\\boxed{\bf~x_2=-3}\\\\\\b)\\|x+5|=-2\\\\|x+5|\geq 0\\\\-2<0\\\\Un~modul~nu~poate~fi~egalat~cu~un~numar~negativ.\\\\\implies~~Ecuatia~"|x+5|=-2"~nu~are~solutie.$

 

Answer 2

a)

|x-1| = 4

x-1 poate lua doua valori, negativa cand x-1 < 0 sau pozitiva cand x-1 ≥ 0.

Cazul I, x-1≥0 => x≥1 => |x-1| = x-1 = 4 => x = 5

Cazul II, x-1<0 => x<1 => |x-1| = -(x-1) = -x+1 = 4 => x=-3

b) |x+5| = -2

Ecuatia nu are solutie deoarece nu are cum sa iasa din modul un nr. negativ.