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DashaLove1119
@DashaLove1119
August 2022
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Пусть x1 и x2 корни уравнения x^2+7x -2=0. Не решая уравнения ,найти x1/x2 + x2/x1.
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akhunovaaliyap6akzm
По теореме Виета: x1+x2=-7, x1•x2=-2, найдём
x1/x2 + x2/x1 = [(x1)^2 + (x2)^2]/[x1•x2] =
=[ (x1)^2 + 2x1•x2 + (x2)^2 - 2x1•x2]/[x1•x2]=
=[ (x1+x2)^2 - 2x1•x2 ] / [x1•x2]=
=[ (-7)^2 - 2 (-2) ] / [-2] = (49+4)/(-2)=-53/2=-26,5
1 votes
Thanks 1
akhunovaaliyap6akzm
Теорема Виета:
akhunovaaliyap6akzm
x^2 + px +q =0
akhunovaaliyap6akzm
x1 +x2 = -p
akhunovaaliyap6akzm
x1•x2 = q
DashaLove1119
Спасибо
akhunovaaliyap6akzm
Не за что)
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Answers & Comments
x1/x2 + x2/x1 = [(x1)^2 + (x2)^2]/[x1•x2] =
=[ (x1)^2 + 2x1•x2 + (x2)^2 - 2x1•x2]/[x1•x2]=
=[ (x1+x2)^2 - 2x1•x2 ] / [x1•x2]=
=[ (-7)^2 - 2 (-2) ] / [-2] = (49+4)/(-2)=-53/2=-26,5