zadanie 47 str 64
Wykonaj podane obliczenia
o)
\sqrt{a-3}*\sqrt{a+3}*\sqrt{a^2-9}, gdy a większe,równe 3
=\sqrt{{(a-3)(a+3)*(a^2-9)}}=\sqrt{{(a^2-9)(a^2-9)}}=a^2-9
zadanie 52 str. 64
Usuń niewymiernośc z mianownika ułamka
h)
\frac{4-2\sqrt5}{6-\sqrt5}=\frac{(4-2\sqrt5)(6+\sqrt5)}{(6-\sqrt5)(6+\sqrt5)}=\frac{24+4\sqrt5-12\sqrt5-2*5}{36-5}=\frac{12-8\sqrt5}{31}
i)
\frac{12}{\sqrt7-\sqrt3}=\frac{12(\sqrt7+\sqrt3)}{(\sqrt7-\sqrt3)(\sqrt7+\sqrt3)}=\frac{12(\sqrt7+\sqrt3)}{7-3}=3(\sqrt7+\sqrt3)
j)
\frac{2\sqrt3-\sqrt5}{\sqrt5-\sqrt3}=\frac{(2\sqrt3-\sqrt5)(\sqrt5+\sqrt3)}{(\sqrt5-\sqrt3)(\sqrt5+\sqrt3)}=\frac{2\sqrt{15}+2\sqrt9-5-\sqrt{15}}{5-3}=\frac{\sqrt{15}+2*3-5}{2}=\frac{\sqrt{15}+1}{2}
k)
\frac{2\sqrt3+\sqrt2}{2\sqrt3-\sqrt2}=\frac{(2\sqrt3+\sqrt2)(2\sqrt3+\sqrt2)}{(2\sqrt3-\sqrt2)(2\sqrt3+\sqrt2)}=\frac{4*3+2\sqrt6+2\sqrt6+2}{4*3-2}=\frac{14+4\sqrt6}{10}=\frac{7+2\sqrt6}{5}