a)
(\sqrt{3+\sqrt5}+\sqrt{3-\sqrt5})^2=(\sqrt{3+\sqrt5})^2+2\sqrt{(3+\sqrt5)(3-\sqrt5}+(\sqrt{3-\sqrt5})^2=
=3+\sqrt5+2\sqrt{9-5}+3-\sqrt5=6+2\sqrt4=6+2*2=10
b)
(\sqrt{2-\sqrt3}-\sqrt{2+\sqrt3})^2=(\sqrt{2-\sqrt3})^2-2\sqrt{(2-\sqrt3)(2+\sqrt3)}+(\sqrt{2+\sqrt3})^2=
=2-\sqrt3-2\sqrt{4-3}+2+\sqrt3=4-2*1=2
wzory skróconego mnożenia:
(a+b)^2=a^2+2ab+b^2
(a-b)^2=a^2-2ab+b^2