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shonya1969101
@shonya1969101
August 2022
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Решить систему уравнений [tex] \left \{ {{2x+3y=21} \atop {2x^2-99=-9y}} \right. [/tex]
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iriska124
3у=21-2х
у=21-2х\3
тогда
2х²-99=-9*(21-2х\3)
2х²-99=-3*(21-2х)
2х²-99=-63+6х
2х²-6х-99+63=0
2х²-6х-36=0
х²-3х-18=0
Д=9-4*1*(-18)=9+72=81=9²
х1=3-9\2=-6\2=-3
х2=3+9\2=12\2=6
теперь зная Х,найдем У
а)у=21-2х\3
х1=-3
у1=21-2*(-3)\3=21+6\3=27\3=9
б)у=21-2х\3
х2=6
у2=21-2*6\3=9\3=3
Ответ------(6,3) или (-3,9)
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Answers & Comments
у=21-2х\3
тогда
2х²-99=-9*(21-2х\3)
2х²-99=-3*(21-2х)
2х²-99=-63+6х
2х²-6х-99+63=0
2х²-6х-36=0
х²-3х-18=0
Д=9-4*1*(-18)=9+72=81=9²
х1=3-9\2=-6\2=-3
х2=3+9\2=12\2=6
теперь зная Х,найдем У
а)у=21-2х\3
х1=-3
у1=21-2*(-3)\3=21+6\3=27\3=9
б)у=21-2х\3
х2=6
у2=21-2*6\3=9\3=3
Ответ------(6,3) или (-3,9)