Produkt

[moth]

1.

Forenkle uttrykket:

[tex](\sqrt{5}+\sqrt{6}+\sqrt{7})(\sqrt{5}+\sqrt{6}-\sqrt{7})(\sqrt{5}-\sqrt{6}+\sqrt{7})(-\sqrt{5}+\sqrt{6}+\sqrt{7})[/tex]

[tex](5+\sqrt{5}\sqrt{6}-\sqrt{5}\sqrt{7}+\sqrt{6}\sqrt{5}+6-\sqrt{6}\sqrt{7}+\sqrt{7}\sqrt{5}+\sqrt{7}\sqrt{6}-7)(-5+\sqrt{5}\sqrt{6}+\sqrt{5}\sqrt{7}+\sqrt{6}\sqrt{5}-6-\sqrt{6}\sqrt{7}-\sqrt{7}\sqrt{5}+\sqrt{7}\sqrt{6}+7)[/tex]

[tex](4+2\sqrt{5}\sqrt{6})(-4+2\sqrt{5}\sqrt{6})[/tex]

[tex]-16+8\sqrt{5}\sqrt{6}-8\sqrt{5}\sqrt{6}+120=\underline{\underline{104}}[/tex]

[BMB]

Stemmer, men fins jo alltids en enklere måte å løse den på.

[moth]

Du må gjerne vise, hvis ingen andre har lyst å prøve seg.

[Klaus Knegg]

[tex](sqrt{5}+sqrt{6}+sqrt{7})(sqrt{5}+sqrt{6}-sqrt{7})(sqrt{5}-sqrt{6}+sqrt{7})(-sqrt{5}+sqrt{6}+sqrt{7})[/tex]
[tex]-((sqrt{5}+sqrt{6})^2-sqrt{7}^2)((sqrt{5}-sqrt{6})^2-sqrt{7}^2)[/tex]

Ekspanderer:
[tex]-(sqrt{5}^2+2\sqrt{5 \cdot 6}+sqrt{6}^2-7)(sqrt{5}^2-2\sqrt{5 \cdot 6}+sqrt{6}^2-7)[/tex]
[tex]-(4+2\sqrt{30})(4-2\sqrt{30})=(2\sqrt{30})^2-4^2=104[/tex]

[BMB]

Det gjør ting en del enklere. ^^