Question

 Rezolvati ecuatiile:( √5-2)x>√20-4  x∈R
x(1-√2) ≥ 4- 2√8, x ∈N
|2x-1|≤3    x∈Z
-1≤2-x≤5     x∈N

Answer 1

(√5-2)x > √20-4
 
(√5-2)x > $2\sqrt{5}$ - 4 

(√5-2)x > 2($\sqrt{5} - 2$ )

x > $\frac{2 ( \sqrt{5} - 2) }{ \sqrt{5} - 2}$

x > 2 
x ∈ intervalului deschis 2 , plus infinit 
----------------------------------------------------------
x(1-√2) ≥ 4- 2√8
[tex]x(1- \sqrt{2} ) \geq 4 - 2*2 \sqrt{2}

x(1- \sqrt{2} ) \geq 4 - 4 \sqrt{2}
 
x(1- \sqrt{2} ) \geq 4(1 - \sqrt{2})
   
x \geq \frac{4(1- \sqrt{2} )}{1 - \sqrt{2} }
   
x \geq 4 [/tex]

x ∈ intervalului inchis 4 , plus infinit 
----------------------------------------------------------

|2x-1|≤3 
$-3 \leq 2x - 1 \leq 3$

Adunam 1 la fiecare termen --> 

-2 ≤ 2x ≤ 4 /:2
-1 ≤ x ≤ 2
x ∈ multimii -1 , 0 , 1 , 2 
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-1≤2-x≤5 
Adunam -2 la fiecare termen --> 
-3 ≤ -x ≤ 3 \(-1)
1 ≥ x ≥ -3 

x ∈ multimii formata din numerele 1 si 0