Question

Rezolvați ecuația:
$\sqrt{({x+4}) ^{2}$=$5- |4+x | ^{2}$
Urgent!

Answer 1

rad( (x+4)^2 )=5-|4+x|^2 =>
=> | x+4|=5- (16+x^2+8*x)<=>
<=>| x+4| = -x^2-8*x -11
cazul 1) x> -4 =>
=> | x+4| = -x^2-8*x -11 <=> x+4= -x^2-8*x -11 <=> x^2+9*x+15=0<=>
delta=81-60=21 => x1= (-9+rad(21))/2
                             x2=(-9-rad(21))/2  
dar x > -4 => x=(-9+rad(21))/2

cazul 2) x < -4  => | x+4| = -x^2-8*x -11 <=>4-x =-x^2-8*x -11<=>
<=>x^2+7*x+15=0 
delta =49-60<0  => nu are solutie in multimea numerelor reale
daca ai invatat nr complexe =>
=>delta = -11  = (rad(11)*i)^2
=> x1=  (-7+rad(11)*i)/2 
     x2=(-7-rad(11)*i)/2