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Determinant

 
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Silvian
Euclid


Joined: 19 Aug 2011
Posts: 12
Location: Bucuresti

PostPosted: Thu Dec 01, 2011 11:21 pm    Post subject: Determinant Reply with quote

Fie determinantul
x1 x2 x3
x2 x3 x1
x3 x1 x2

x1,x2,x3 e R sunt solutiile ecuatiei x^3-2x=0

sa se calculeze x1,x2,x3
x1^2+x2^2+x3^2
c)sa se calculeze determinantul d
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Mateescu Constantin
Newton


Joined: 21 Apr 2009
Posts: 398
Location: Londra/Pitesti

PostPosted: Thu Dec 01, 2011 11:36 pm    Post subject: Reply with quote

Probleme ca cea de mai sus se incadreaza la sectiunea "Matematica la clasa", respectiv la Clasa a XI-a ... In plus, nu ar strica daca ai invata si putin \LaTeX ...

Se observa ca x^3-2x=x\left(x+\sqrt 2\right)\left(x-\sqrt 2\right)=0 , de unde x_1=-\sqrt 2 , x_2=0 , x_3=\sqrt 2 . Apoi x_1^2+x_2^2+x_3^2=4, iar \left|\begin{array}{cccc}
-\sqrt 2 && 0 && \sqrt 2 \\\\\\\\ 
0 && \sqrt 2 && -\sqrt 2 \\\\\\\\ 
\sqrt 2 && -\sqrt 2 && 0\end{array}\right|=0 ...
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Virgil Nicula
Euler


Joined: 28 Sep 2007
Posts: 672

PostPosted: Sat Dec 03, 2011 3:59 pm    Post subject: Reply with quote

See PP3 from here (<== click).
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