Zadanie Oblicz. ( \sqrt{5- \sqrt{7}} + \sqrt{5+ \sqrt{7} } )^2
źródło:
(\sqrt{5-\sqrt{7}}+\sqrt{5+\sqrt{7}})^2=(\sqrt{5-\sqrt7})^2+2\sqrt{(5-\sqrt7)(5+\sqrt7)}+(\sqrt{5+\sqrt7})^2=5-\sqrt7+2\sqrt{25-7}+5+\sqrt7=10+2\sqrt{18}=10+2\sqrt{9*2}=10+2*3\sqrt2=10+6\sqrt2