Question

a = √2 + 1/ 2 b= 2/ √2- 1
Trebuie sa aratati ca b/a - a/b = 15/4
Cu explicatii, va rog !

Answer 1

[tex]a=\frac{\sqrt{2}+1}{2}\\ b=\frac{2}{\sqrt{2}-1}\\ \frac{b}{a}=\frac{2}{\sqrt{2}-1}\cdot\frac{2}{\sqrt{2}+1}=\frac{4}{2-1}=4\\ [/tex]
[tex]\frac{a}{b}=\frac{\sqrt{2}+1}{2}\cdot\frac{\sqrt{2}-1}{2}=\frac{2-1}{4}=\frac{1}{4}\\ \frac{b}{a}-\frac{a}{b}=4-\frac{1}{4}=\frac{16}{4}-\frac{1}{4}=\frac{15}{4}[/tex]