Question

Calculati |√5 - 3 | supra 3 + |2- √5| supra 2 - 1 pe 3 * radical din 5 pe 2

Answer 1

    
[tex] \displaystyle \frac{| \sqrt{5} -3|}{3} + \frac{|2- \sqrt{5}|}{2} - \frac{1}{3} \cdot \frac{ \sqrt{5}}{2} = ~~~(unde ~2 \ \textless \ \sqrt{5} \ \textless \ 3 ) \\ \\ =\frac{3- \sqrt{5}}{3} + \frac{ \sqrt{5}-2}{2} - \frac{1}{3} \cdot \frac{ \sqrt{5}}{2}= \\ \\ =\frac{(3- \sqrt{5}) \times 2}{3 \times 2} + \frac{( \sqrt{5}-2) \times 3}{2 \times 3} - \frac{1 \times \sqrt{5}}{3 \times 2}= \\ \\ =\frac{(6- 2\sqrt{5})}{6} + \frac{(3\sqrt{5}-6)}{6} - \frac{ \sqrt{5}}{6}=[/tex]

[tex]\displaystyle = \frac{6- 2\sqrt{5}}{6} + \frac{3\sqrt{5}-6}{6} - \frac{ \sqrt{5}}{6}= \\ \\ =\frac{6- 2\sqrt{5} +3\sqrt{5}-6 -\sqrt{5}}{6}= \\ \\ =\frac{6-6 +3\sqrt{5} - 2\sqrt{5} -\sqrt{5}}{6}= \frac{0+0\sqrt{5}}{6} =\boxed{0}[/tex]