Răspuns :
[tex]1) \\ 7-2x\ \textgreater \ \sqrt{2} \\ -2x\ \textgreater \ \sqrt{2}-7\;\;\;\;|\;\cdot (-1) \\ 2x \ \textless \ 7-\sqrt{2} \\ x\ \textless \ \frac{7-\sqrt{2}}{2} \\ x\ \textless \ \frac{7}{2} -\frac{\sqrt{2}}{2} \\ x\ \textless \ \frac{7}{2} -\frac{1,41}{2} \\ x\ \textless \ 3,5 -0,705 \\ x\ \textless \ 2,795 \\ A=\{0;\;1;\;2 \}[/tex]
[tex]2) \\ \sqrt{4}- \sqrt{7}\;\cdot\; \sqrt{4}+\sqrt{7}= 2-\underline{2\sqrt{7}}+\underline{\sqrt{7}}=\boxed{2-\sqrt{7}} \\ \\ \\ 3) \\ 4x^2=9 \\ x^2= \frac{9}{4} \\ x_{12}= \pm\sqrt{\frac{9}{4}} = \pm\frac{3}{2}\\ x_1 = \boxed{\frac{3}{2}} \\ x_2 = \boxed{-\frac{3}{2}}[/tex]
[tex]4) \\ Notatie: \\ a;\;b;\;c = laturile \;triunghiului \\ \\ Rezolvare: \\ \frac{a}{5} = \frac{b}{12} = \frac{c}{13} =k \\ a=5k \\ b=12k \\ c=13k \\ \text{Verificam daca a, b, c verifica formula: }a^2 + b^2 = c^2 \\ \boxed{a^2 + b^2}= (5k)^2+(12k)^2 = 25k^2+144k^2 = 169k^2 = (13k)^2 = \boxed{c^2} \\ =\ \textgreater \ \;\; \boxed{a^2 + b^2=c^2} \\ =\ \textgreater \ \;\; \boxed{\text{Triunghiul este dreptunghic}}[/tex]
