[tex]f(x) = (3-2\sqrt{2})x+12\sqrt{2}\\\\\\f(\frac{1}{3+2\sqrt{2}})= (3-2\sqrt{2})\cdot\frac{1}{3+2\sqrt{2}}+12\sqrt{12}=\frac{3-2\sqrt{2}}{3+2\sqrt{2}}\cdot\frac{3-\sqrt{2}}{3-2\sqrt{2}}+12\sqrt{2} =\\\\= \frac{(3-2\sqrt{2})^{2}}{(3+2\sqrt{2})(3-2\sqrt{2})}+12\sqrt{12}=\frac{9-12\sqrt{2}+8}{9-8}+12\sqrt{2} = \frac{17-12\sqrt{2}}{1}+12\sqrt{2}=\\\\=17-12\sqrt{2}+12\sqrt{2}=17\\\\\underline{17} \ \ \rightarrow \ \ liczba \ pierwsza\\\\Odp. \ A.[/tex]
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Wykorzystano wzory:
[tex](a-b)^{2} = a^{2}-2ab + b^{2}\\\\(a+b)(a-b) = a^{2}-b^{2}[/tex]
