Odpowiedź:
a = 5 - 4[tex]\sqrt{2}[/tex], b = 5 + 4[tex]\sqrt{2}[/tex]
a) Iloczyn = mnożenie:
(5 - 4[tex]\sqrt{2}[/tex]) × (5 + 4[tex]\sqrt{2}[/tex]) = 5² - (4[tex]\sqrt{2}}[/tex])² = 25 - 32 = -7
b) Iloraz = dzielenie:
[tex]\frac{5-4\sqrt{2} }{5+4\sqrt{2} }[/tex] = [tex]\frac{5-4\sqrt{2} }{5+4\sqrt{2} }[/tex] × [tex]\frac{5-4\sqrt{2} }{5-4\sqrt{2}}[/tex] = [tex]\frac{(5-4\sqrt{2})(5-4\sqrt{2}) }{-7}[/tex] = [tex]\frac{25 - 20\sqrt{2} - 20\sqrt{2} + 32}{-7}[/tex] = [tex]\frac{57-40\sqrt{2} }{-7}[/tex]