Usuń niewymierność:.... Question from @lasalila

September 2018 2 26 Report

Usuń niewymierność:
$\frac{1}{2(1+\sqrt{2})}+\frac{1}{2(1-\sqrt{2})}$

Roma

$\frac{1}{2(1+\sqrt{2})}+\frac{1}{2(1-\sqrt{2})} = \frac{1-\sqrt{2}}{2(1+\sqrt{2})(1-\sqrt{2})}+\frac{1+\sqrt{2}}{2(1-\sqrt{2})(1+\sqrt{2})} =$

$= \frac{1-\sqrt{2}+1+\sqrt{2}}{2(1+\sqrt{2})(1-\sqrt{2})} = \frac{2}{2 \cdot [1^2-(\sqrt{2})^2]} = \frac{2}{2 \cdot (1-2)} = \frac{2}{2 \cdot (- 1)} = \frac{2}{-2} = - 1$

1 votes Thanks 1

basetla

1/[2(1+V2)] + 1/[2(1-V2)] = 1/[2(1+V2)] * (1-V2)/(1-V2) + 1/[2(1-V2)] *(1+V2)/(1-V3) =

= (1-V2)/2(1-2) + (1+V2)/2(1-2) = (1-V2+1+V2)/(-2) = 2/(-2) = -1

0 votes Thanks 0

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