Question

Sa se rezolve ecuatia :
|x+4|+ |16- x patrat | = 0

Answer 1

pt ca o suma de modulesa fie 0 , ambele module trebuiesa fie 0

x+4=0...x=-4

x²-16=0..x=4 sau x=-4

convine doar x=-4, careverifica ambele ecuatii

sau altfel scris {-4}∩{-4;4}={-4}

Answer 2

$\it |x+4| +|16-x^2| =0\Rightarrow |x+4| +|4^2-x^2| = 0 \Rightarrow |x+4| +|x^2-4^2|=0\Rightarrow\\ \\ \\ \Rightarrow |x+4| +|(x+4)(x-4)| =0\Rightarrow |x+4| +|x+4|\cdot|x-4| =0 \Rightarrow\\ \\ \\ \Rightarrow |x+4|(1+|x-4|) =0 \ \ \ \ (1)$

$\it |x-4| \geq0 |_{+1}\ \Rightarrow 1+|x-4| \geq1\geq0\ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow |x-4| =0 \Rightarrow x+4=0 \Rightarrow x = -4$