Question

Rezolvați ecuațiile
a) |x+4|+x^2 -4xy +4y^2=0
b) (radical2 +1)x +(3radical2 +1)y -5radical2-1 =0, unde x si y aparțin Q
c) |x-2| + |y+5| + |x+y+z| =0

Answer 1

Suma a 2 expresii pzitive = 0  daca fiecare expresie = 0
a) |x+4|+x^2 -4xy +4y^2=0  => |x+4|+ (x - 2y)^2 =0   |x+4| = 0  => x + 4 = 0  => x = -4   (x - 2y)^2 =0  => x - 2y = 0  =>  -4 - 2y = 0  => y = -2
b) Nu ies ambele necunoscute In Q; poate e ceva gresit
c) |x-2| + |y+5| + |x+y+z| =0
  |x-2| = 0  => x-2 = 0  => x = 2
  |y+5| = 0 =>  y + 5 = 0 => y = -5
 |x+y+z| =0  => x+y+z = 0 => 2 -5 +z = 0  => z = 3