Observam
(3-2√2)(3+2√2)=9-8=1
Deci
[tex]3-2\sqrt{2} =\frac{1}{3+2\sqrt{2} }[/tex]
Notam
[tex](\sqrt[4]{3-2\sqrt{2} } )^x=t\\\\(\sqrt[4]{3+2\sqrt{2} } )^x=\frac{1}{t} \\\\[/tex]
[tex]t+\frac{1}{t} =\frac{5}{2}[/tex]
2t²+2-5t=0
2t²-5t+2=0
Δ=25-16=9
[tex]t_1=\frac{5+3}{4} =2\\\\t_2=\frac{5-3}{4} =\frac{1}{2}[/tex]
