Odpowiedź:
[tex]a_1=\sqrt{2} \\a_2=4-\sqrt{2} \\\displaystyle q=\frac{a_2}{a_1} =\frac{4-\sqrt{2} }{\sqrt{2} } \cdot\frac{\sqrt{2} }{\sqrt{2} } =\frac{4\sqrt{2}-2 }{2} =2\sqrt{2} -1\\a_3=a_2\cdot q=(4-\sqrt{2} )(2\sqrt{2} -1)=8\sqrt{2} -4-4+\sqrt{2} =9\sqrt{2} -8\\a_4=a_3\cdot q=(9\sqrt{2} -8)(2\sqrt{2} -1)=36-9\sqrt{2} -16\sqrt{2} +8=\\\underline{44-25\sqrt{2} }[/tex]
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Odpowiedź:
[tex]a_1=\sqrt{2} \\a_2=4-\sqrt{2} \\\displaystyle q=\frac{a_2}{a_1} =\frac{4-\sqrt{2} }{\sqrt{2} } \cdot\frac{\sqrt{2} }{\sqrt{2} } =\frac{4\sqrt{2}-2 }{2} =2\sqrt{2} -1\\a_3=a_2\cdot q=(4-\sqrt{2} )(2\sqrt{2} -1)=8\sqrt{2} -4-4+\sqrt{2} =9\sqrt{2} -8\\a_4=a_3\cdot q=(9\sqrt{2} -8)(2\sqrt{2} -1)=36-9\sqrt{2} -16\sqrt{2} +8=\\\underline{44-25\sqrt{2} }[/tex]