$F=\sqrt{\dfrac{3-\sqrt 5}{2}}-\sqrt{\dfrac{3+\sqrt 5}{2}}\\↔2F=\sqrt 4.\left(\sqrt{\dfrac{3-\sqrt 5}{2}}-\sqrt{\dfrac{3+\sqrt 5}{2}}\right)\\↔2F=\sqrt 2(\sqrt{3-\sqrt 5}-\sqrt{3+\sqrt 5})\\↔2F=\sqrt{2(3-\sqrt 5)}-\sqrt{2(3+\sqrt 5)}\\↔2F=\sqrt{6-2\sqrt 5}-\sqrt{6+2\sqrt 5}\\↔2F=\sqrt{5-2\sqrt 5+1}-\sqrt{5+2\sqrt 5+1}\\↔2F=\sqrt{(\sqrt 5-1)^2}-\sqrt{(\sqrt 5+1)^2}\\↔2F=|\sqrt 5-1|-|\sqrt 5+1|\\↔2F=\sqrt 5-1-\sqrt 5-1\\↔2F=-2\\↔F=-1$
Vậy $F=-1$
