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MarieSwan
@MarieSwan
July 2022
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20 баллов. Алгебра, 8 класс. Задания на картинке. С решением! 7 задание не обязательно
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oganesbagoyan
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4. (2y -5)/(y+5) = (3y+21)/(2y -1);
ОДЗ : { y ≠ -5 ; y ≠ 1/2.
(2y -5)(2y -1)=(3y+21)(y+5) ;
4y² -12y +5 =3y² +36y +105 ;
y² -48y -100=0 ; D/4 =(48/2)² -(-100) =676 =26²
y₁ =24 -26 = -2 ;
y
₂ =24 +26 =50 .
(y₁+y₂) / 2 =(-2+50)/2 = 24
ответ: Г)24
-----
5.
(3x² -5x -2) /( 2 -x) =0 ;
ОДЗ : x≠2.
3x² -5x -2 =0 ; D =5² -4*3(-2) =49=7² ;
x₁ =(5+7)/ (2*3 ) =2 ∉ ОДЗ
x₂ =(5-7)/ 6 = -1/3
ответ: Г) -1/3
---
6. (a-14) / (a³ -8) = 5/ (a²+2a+4) -1/(a-2) ;
* * * a³ -8 =a³ -2³ =(a - 2)(a²+2a+4) * * *
ОДЗ : x≠2.
a-14 = 5(a-2) - (a²+2a+4) ;
a-14 = 5a-10 - a²-2a-4 ;
a² -2a =0 ;
a(a-2) =0 ;
a =2 ∉ ОДЗ ;
ответ: a=0.
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Answers & Comments
Verified answer
4. (2y -5)/(y+5) = (3y+21)/(2y -1);ОДЗ : { y ≠ -5 ; y ≠ 1/2.
(2y -5)(2y -1)=(3y+21)(y+5) ;
4y² -12y +5 =3y² +36y +105 ;
y² -48y -100=0 ; D/4 =(48/2)² -(-100) =676 =26²
y₁ =24 -26 = -2 ;
y₂ =24 +26 =50 .
(y₁+y₂) / 2 =(-2+50)/2 = 24
ответ: Г)24
-----
5.
(3x² -5x -2) /( 2 -x) =0 ;
ОДЗ : x≠2.
3x² -5x -2 =0 ; D =5² -4*3(-2) =49=7² ;
x₁ =(5+7)/ (2*3 ) =2 ∉ ОДЗ
x₂ =(5-7)/ 6 = -1/3
ответ: Г) -1/3
---
6. (a-14) / (a³ -8) = 5/ (a²+2a+4) -1/(a-2) ;
* * * a³ -8 =a³ -2³ =(a - 2)(a²+2a+4) * * *
ОДЗ : x≠2.
a-14 = 5(a-2) - (a²+2a+4) ;
a-14 = 5a-10 - a²-2a-4 ;
a² -2a =0 ;
a(a-2) =0 ;
a =2 ∉ ОДЗ ;
ответ: a=0.