Question

Care este multimea solutiilor inecuatiei $\sqrt{x+3} + \sqrt{2-x} \leq 3$

Answer 1

rad(x+3) +rad(2-x) <= 3
rad(x+3) +rad(2-x)-3<= 0
rad(x+3) +rad(2-x)-3 =0
rad(x+3) +rad(2-x)=3 ()^2
C.E :
x+3 >=0 , x € [-3,+inf)
2-x >=0 , x € (-inf,2]
D : x € [-3,+inf)

x+3+2rad[(x+3)(2-x)]+2-x=9
2rad[(x+3)(2-x)]=4 /:2
rad[(x+3)(2-x)]=2 ()^2
(x+3)(2-x)=4
2x-x^2+6-3x=4
-x^2-x+2=0 /*(-1)
x^2+x-2=0 ( d= delta )
d=1+8 =9 =>rad(d) =3
x1= -2 ; x2 = 1
x1,x2 € [-3,+inf) => S:{-2,1}

Answer 2

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