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Aliya1000
@Aliya1000
July 2022
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решите пож по алгебре с помошью систимы уравнения 9 класс
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oganesbagoyan
Verified answer
1)
{ x +y =10 ; x² -y² =40 ⇔{ x +y =10 ; (x +y)(x-y) =40⇔ { x +y =10 ; 10(x-y) =40.
{ x+y =10 ; x -y =4 . || уравнения ""+"" и "-"" ||
{ x =7 ; y =3.
----------------
2)
{ x -5y =9 ; x² +xy -3y² =27.
{ x =5y +9 ; (5y +9)² +(5y +9)y - 3y² =27.
25y² +90y +81 +5y² +9y - 3y² =27.
27y² +99y +54 =0 ;
3y² +11y +6 =0 ;
D =11² -4*3*6 =49 =7² ;√D =7 .
y₁,₂ = (-11
± 7)/2*3 .
y
₁
= (-11 -7)/6
= - 3
⇒
x₁
=5y +9 =5*(-3) +9
= -6 .
y
₂
=(-11+7)/6
= -2/3
⇒
x₂
=5y+9 = 5*(-2/3) +9
=17/3.
ответ : {( -6 ; -3)
, (17/3 ; -2/3) }.
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Answers & Comments
Verified answer
1) { x +y =10 ; x² -y² =40 ⇔{ x +y =10 ; (x +y)(x-y) =40⇔ { x +y =10 ; 10(x-y) =40.{ x+y =10 ; x -y =4 . || уравнения ""+"" и "-"" ||
{ x =7 ; y =3.
----------------
2) { x -5y =9 ; x² +xy -3y² =27.
{ x =5y +9 ; (5y +9)² +(5y +9)y - 3y² =27.
25y² +90y +81 +5y² +9y - 3y² =27.
27y² +99y +54 =0 ;
3y² +11y +6 =0 ;
D =11² -4*3*6 =49 =7² ;√D =7 .
y₁,₂ = (-11 ± 7)/2*3 .
y₁ = (-11 -7)/6 = - 3 ⇒x₁ =5y +9 =5*(-3) +9 = -6 .
y₂ =(-11+7)/6 = -2/3⇒x₂ =5y+9 = 5*(-2/3) +9 =17/3.
ответ : {( -6 ; -3) , (17/3 ; -2/3) }.