Verified answer

Vom introduce sub radical, apoi va fi ușor de determinat valorile elementelor:

a) A = {x ∈ N | 3 ≤ √x < 4}

[tex]3 \leq \sqrt{x} < 4 \Rightarrow \sqrt{9} \leq \sqrt{x} < \sqrt{16} \\[/tex]

[tex]x \in \Bbb{N} \Rightarrow \boldsymbol{A = \{9,10,11,12,13,14,15\}}\\[/tex]

b) B = {x ∈ N | -5 ≤ - √x ≤ -4}

[tex]-5 \leq -\sqrt{x} \leq -4 \Rightarrow -\sqrt{25} \leq -\sqrt{x} < -\sqrt{16} \\[/tex]

[tex]x \in \Bbb{N} \Rightarrow \boldsymbol{B = \{16,17,18,19,20,21,22,23,24,25\}}\\[/tex]

Vom determina pătratele perfecte între care ia valori x²:

c) C = {x ∈ N | 32 ≤ 2[tex]x^{2}[/tex] ≤ 98}

[tex]32 \leq 2x^{2} \leq 98 \ \ \Big|:2 \Rightarrow 16 \leq x^{2} \leq 49\\[/tex]

[tex]\Rightarrow 4^{2} \leq x^{2} \leq 7^{2}[/tex]

[tex]x \in \Bbb{N} \Rightarrow \boldsymbol{C = \{4,5,6,7\}}\\[/tex]

d) D = {x ∈ N | 15 ≤ [tex]x^{2}[/tex] ≤ 81}

[tex]15 \leq x^{2} \leq 81 \ \Rightarrow \ 15 < 16 \leq x^{2} \leq 81\\[/tex]

[tex]\Rightarrow 4^{2} \leq x^{2} \leq 9^{2}[/tex]

[tex]x \in \Bbb{N} \Rightarrow \boldsymbol{D = \{4,5,6,7,8,9\}}\\[/tex]