Question

Radical x+2 plus radical 3-x egal 3

Answer 1

$\sqrt{x+2}+ \sqrt{3-x} =3$
Cond: 
x+2≥0=> x≥-2 =>x ∈[-2;+∞) 
3-x≥0 <=> -x≥-3 <=> x≤3 =>x∈(-∞;3 ]
=> x∈[-2;3]
Ridicam la patrat  si obt: 
x+2 +3-x +2($\sqrt{(x+2)(3-x)}$=9
<=> 5+2$\sqrt{(-x^2+x+6)}$=9<=>  2$\sqrt{(-x^2+x+6)}$=4 |2 <=> 4(-x²+x+6)= 16 |:4 <=>  -x²+x+6= 4 |(-1)<=> x²-x-2=0
Δ=1+8= 9 => √Δ=3
x1=2 si x2= -1  
S={-1; 2}