Odpowiedź:
3/√11= 3*√11 / √11*√11 = 3√11 / 11
3/√7 + 3 = 3*(√7-3)/ (√7+3)*(√7-3) = 3√7 - 9 / 7 - 9 = 3√7 - 9 / -2
5√5/2√5 - 3 = 5√5 * (2√5 + 3) / (2√5 - 3) * (2√5 + 3) = 50 + 15√5 / 20 - 9 = 50 + 15√5 / 11
Szczegółowe wyjaśnienie:
Odpowiedź:
[tex]\dfrac{3}{\sqrt{11}}=\dfrac{3}{\sqrt{11}}*\dfrac{\sqrt{11}}{\sqrt{11}}=\dfrac{3\sqrt{11}}{11}\\\\\\\\\dfrac{3}{\sqrt{7}+3}=\dfrac{3}{\sqrt{7}+3}*\dfrac{\sqrt{7}-3}{\sqrt{7}-3}=\dfrac{3(\sqrt{7}-3)}{(\sqrt{7}+3)(\sqrt{7}-3)}=\dfrac{3\sqrt{7}-9}{(\sqrt{7})^2-3^2}=\dfrac{3\sqrt{7}-9}{7-9}=\\\\\\=\dfrac{3\sqrt{7}-9}{-2}=-\dfrac{3\sqrt{7}-9}{2}[/tex]
[tex]\dfrac{5\sqrt{5}}{2\sqrt{5}-3}=\dfrac{5\sqrt{5}}{2\sqrt{5}-3}*\dfrac{2\sqrt{5}+3}{2\sqrt{5}+3}=\dfrac{5\sqrt{5}(2\sqrt{5}+3)}{(2\sqrt{5}-3)(2\sqrt{5}+3)}=\dfrac{10*5+15\sqrt{5}}{(2\sqrt{5})^2-3^2}=\\\\\\=\dfrac{50+15\sqrt{5}}{4*5-9}=\dfrac{50+15\sqrt{5}}{20-9}=\dfrac{50+15\sqrt{5}}{11}[/tex]
