Zadanie 54
a)
(\sqrt{21}-\sqrt{20})(\sqrt{21}+\sqrt{20})=(\sqrt{21})^2-(\sqrt{20})^2=21-20=1
b)
{\sqrt{\sqrt{13}+2}*\sqrt{\sqrt{13}-2}=\sqrt{(\sqrt{13}+2)(\sqrt{13}-2)}=\sqrt{(\sqrt{13})^2-2^2}=\sqrt{13-4}=\sqrt9=3}
c)
{\sqrt{5\sqrt2+7}*\sqrt{5\sqrt2-7}=\sqrt{(5\sqrt2+7)*(5\sqrt2-7)}=\sqrt{(5\sqrt2)^2-7^2}=\sqrt{25*2-49}=\sqrt{1}=1}
Zadanie 55
a)
{\frac{1}{1-\sqrt2}*\frac{1}{1+\sqrt2}=\frac{1}{(1-\sqrt2)(1+\sqrt2)}=\frac{1}{1^2-(\sqrt2)^2}=\frac{1}{1-2}=\frac{1}{-1}=-1}
b)
\frac{1}{\sqrt5+2}*\frac{1}{\sqrt5-2}=\frac{1}{(\sqrt5+2)(\sqrt5-2)}=\frac{1}{(\sqrt5)^2-2^2}=\frac{1}{5-4}=1
c)
{\frac{1}{\sqrt5+\sqrt2}*\frac{1}{\sqrt5-\sqrt2}=\frac{1}{(\sqrt5+\sqrt2)(\sqrt5-\sqrt22)}=\frac{1}{(\sqrt5)^2-(\sqrt2)^2}=\frac{1}{5-2}=\frac{1}{3}}
wzór skróconego mnożenia
(a-b)(a+b)=a^2-b^2