Zadanie 1 usuń niewymiernosc z mianownika podpunkt d Zadanie 2 oblicz wartość liczbowa podpunkt c

[latex]dfrac{3}{sqrt{13}+sqrt{10}}=dfrac{3cdot(sqrt{13}-sqrt{10})}{(sqrt{13}+sqrt{10})cdot(sqrt{13}-sqrt{10})}=\\{}\=dfrac{3cdot(sqrt{13}-sqrt{10})}{13-10}=dfrac{3cdot(sqrt{13}-sqrt{10})}{3}=sqrt{13}-sqrt{10}[/latex] [latex]dfrac{2}{4+2sqrt5}-dfrac{6}{4-2sqrt5}=dfrac{2cdot(4-2sqrt5)}{16-4cdot5}-dfrac{6cdot(4+2sqrt5)}{16-4cdot5}=\\{}\=dfrac{8-4sqrt5-24-12sqrt5}{-4}=dfrac{-16-16sqrt5}{-4}=4+4sqrt5[/latex]

[latex]d)\\frac{3}{sqrt{13}+sqrt{10}}*frac{sqrt{13}-sqrt{10}}{sqrt{13}-sqrt{10}} = frac{3(sqrt{13}-sqrt{10})}{13-10} = frac{3(sqrt{13}-sqrt{10})}{3} = sqrt{13}-sqrt{10}[/latex] [latex]c)\\frac{2}{4+2sqrt{5}}-frac{6}{4-2sqrt{5}} = frac{2(4-2sqrt{5})-6(4+2sqrt{5})}{(4+2sqrt{5})(4-2sqrt{5})} = frac{8-4sqrt{5}-24-12sqrt{5}}{16-20}=frac{-16-16sqrt{5}}{-4} =\\=frac{-4(4+4sqrt{5})}{-4} = 4+4sqrt{5} = 4(1+sqrt{5})[/latex]