1) Wyznacz liczbę odwrotną do "x" gdy; a) x=4+2√7 b) x=3-√5 c) x=2√3+2 2)Skróć ułamki; a)4-8√5/6+12√5 b)-5-10√2/2√2+1 c)2√3-6/4√3+2 d)2√3+4√6/2√3

Zad.1[latex]a) x=4+2sqrt{7}\ frac{1}{x}=frac{1}{4+2sqrt{7}} cdot frac{4-2sqrt{7}}{4-2sqrt{7}} = frac{4-2sqrt{7}}{16-28}=frac{-2(sqrt{7}-2)}{-12}=frac{sqrt{7}-2}{6}\ \ b) x=3-sqrt{5}\ frac{1}{x}=frac{1}{3-sqrt{5}}cdot frac{3+sqrt{5}}{3+sqrt{5}}=frac{3+sqrt{5}}{9-5}=frac{3+sqrt{5}}4}\ \ \ c) x=2sqrt{3}+2\ frac{1}{x}=frac{1}{2sqrt{3}+2}cdot frac{2sqrt{3}-2}{2sqrt{3}-2}=frac{2sqrt{3}-2}{12-4}=frac{2(sqrt{3}-1)}{8}=frac{sqrt{3}-1}{4}[/latex]Zad.2[latex]a) frac{4-8sqrt{5}}{6+12sqrt{5}} = frac{-4(2sqrt{5}+1)}{6(1+2sqrt{5})}=-frac{4}{6}=-frac{2}{3}\ \ b) frac{-5-10sqrt{2}}{2sqrt{2}+1}=frac{-5(1+2sqrt{2})}{2sqrt{2}+1}=-5\ \ c) frac{2sqrt{3}-6}{4sqrt{3}+2}=frac{2(sqrt{3}-3)}{2(2sqrt{3}+1)}=frac{sqrt{3}-3}{2sqrt{3}+1}cdot frac{2sqrt{3}-1}{2sqrt{3}-1}=frac{6-sqrt{3}-6sqrt{3}+3}{12-1}=frac{9-7sqrt{3}}{11}\ \ d) frac{2sqrt{3}+4sqrt{6}}{2sqrt{3}}=frac{2sqrt{3}(1+2sqrt{2})}{2sqrt{3}}=1+2sqrt{2}[/latex]