Task/25769243
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Решить уравнения
1) { x ² +2xy +y² =49 ; { (x+y)² =7²; { x+y =±7;
{ x -y = 3 . { x -y =3. { x-y =3 .
a) { x+y =-7 ; { 2x =(-7)+(3) ; { x = - 2 ;
{ x-y = 3. {2y =( -7) -(-3) . { y = - 5.
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b) { x+y =7 ; { 2x =7+3 ; { x =5 ;
{ x- y = 3. {2y =7 -3 . { y =2.
ответ : (-2 ; -5) , (5;2) .
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2) x/(x+4) +x/(x-4) =5 5/9 ; * * * 5 5/9 = (5*9+5)/9 =50/9 * * *
x(x -4) +x(x+4) =(50/9)* (x-4)*(x+4) ; * * * (x-4)(x+4) = x² -4² =x² -16 * * *
9 (x² - 4x +x² +4x) =50*(x² -16) ;
9*2x² =50*(x² -16) ;
9x² =25x² - 25*16
16x² =25*16 ;
x² =25 ;
x = ± 5.
ответ : - 5 , 5 .