Срочно...прошу...хотя бы несколько. Created by Яшыч. algebra-ru

Срочно...прошу...хотя бы несколько...

Яшыч @Яшыч

July 2022 1 2 Report

Срочно...прошу...хотя бы несколько

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zhenyaM2002

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А)
х²/(х-2) + 2х/(2-х) = 5
х²/(х-2) - 2х/(х-2) = 5 | *(x-2)
знаменатель ≠ 0 ⇒ x - 2 ≠ 0  ⇒ х ≠ 2
х² - 2х = 5*(х - 2)
х² - 2х = 5х - 10
х² - 2х - 5х + 10 = 0
х² - 7х + 10 = 0
D = (-7)² - 4*1 * 10 = 49 - 40 = 9 = 3²
D>0
x₁ = ( - (-7) - 3) /(2*1) = (7 - 3) / 2 = 4/2 = 2 посторонний корень ( х≠2 )
x₂ = ( - (-7) + 3) / (2*1) = (7 + 3) /2 = 10/2 = 5

проверка:
5²/(5-2) + (2*5)/ ( 2-5) = 25/3 + 10/(-3) = 25/3 - 10/3 = 15/3 = 5

Ответ : х = 5.

б)
х²/(х-1) - 3х/(1-х) = 3х + 4
х²/(х-1) + 3х/(х - 1) = 3х + 4 |*(x-1)
x- 1≠ 0  ⇒ x ≠ 1
x² + 3x = (3x + 4)(x - 1)
x² + 3x = 3x² - 3x + 4x - 4
x² + 3x = 3x² + x -4
3x² +x - 4 -x² - 3x = 0
2x² - 2x - 4 = 0
2(x² - x - 2) = 0 |÷2
x² - x - 2 = 0
D = (-1)² - 4*1*(-2) = 1 + 8 = 9 = 3²
D>0
x₁ = ( -(-1) - 3) /(2*1) = (1 - 3) /2 = - 2/2 = - 1
x₂ = ( - (-1) +3) /(2*1) = (1 + 3)/2 = 4/2 = 2

проверка:
(-1)²/(-1-1) - 3*(-1)/ (1 - (-1) )= 3 *(-1) + 4
- 1/2 - ( -3)/2 = - 3 + 4
-1/2 + 3/2 = 1
1 = 1

2²/(2 -1) - 3*2/(1 - 2) = 3*2 + 4
4/1 - 6/(-1) = 6 + 4
4 + 6 = 10
10=10
Ответ: х₁ = - 1 ; х₂ = 2

в)
(t - 3)/t - 1 = (t+5)/(t-3) | *t(t-3)
t≠0 ;   t≠3
(t - 3)(t-3) - 1*t(t-3) = (t+5) * t
t² - 6t + 3² - t² + 3t = t² + 5t
- 3t + 9 = t² + 5t
t² + 5t + 3t - 9 = 0
t² + 8t - 9 = 0
D = 8² - 4*1*(-9) = 64 + 36 = 100 = 10²
x₁ = ( - 8 - 10)/(2*1) = - 18/2 = - 9
x₂ = ( - 8 + 10) / (2*1) = 2/2 = 1

проверка:
(-9-3)/ (-9) - 1 = (-9+5)/(-9 - 3)
-12/ (-9) - 1 = (- 4) /(-12)
1 ц. 1/3 - 1 = 1/3
1/3 = 1/3

(1-3)/1 - 1 = (1 + 5)/(1-3)
- 2 - 1 = 6/(-2)
-3 = -3
Ответ: х₁ = - 9 ; х ₂ = 1

г)
(5х² + 2х - 24) / (х - 5) = 0
х - 5≠ 0  ⇒ х≠ 5
5х² + 2х - 24 = 0
D = 2² - 4*5*(-24) = 4 +480 = 484 = 22²
D> 0
x₁ = ( - 2 - 22)/(2*5) = -24/10 = - 2.4
x₂ = (-2 + 22)/(2*5)= 20/10 = 2

проверка:
(5 (- 2,4)² + 2(-2,4) - 24) / (-2,4*5) = (28,8 - 4,8 - 24) /(- 12) = 0/(-12) = 0
( 5*2² + 2*2 - 24) /(2*5) = (20 + 4 - 24) /10 = 0/10 = 0

Ответ : х₁ = - 2,4 ; х₂ = 2 .
Думаю, достаточно...

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