Răspuns:
a=√3+2√2 ⇒ [tex]\frac{1}{a}=\frac{1}{\sqrt{3}+2\sqrt{2}} =\frac{\sqrt{3}-2\sqrt{2}}{3-8} =\frac{\sqrt{3}-2\sqrt{2}}{-5}[/tex]
b=√3-2√2 ⇒ [tex]\frac{1}{b}=\frac{1}{\sqrt{3}-2\sqrt{2}} =\frac{\sqrt{3}+2\sqrt{2}}{3-8} =\frac{\sqrt{3}+2\sqrt{2}}{-5}[/tex]
[tex]\frac{1}{a}-\frac{1}{b}=\frac{\sqrt{3}-2\sqrt{2}}{-5}-\frac{\sqrt{3}+2\sqrt{2}}{-5}=\frac{-4\sqrt{2}}{-5}=\frac{4\sqrt{2}}{5}[/tex] ∉ Z
Explicație pas cu pas: