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VladimirLK
@VladimirLK
August 2022
1
8
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решите пж срочно. Все, там 2 задание решите методом интервала
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oganesbagoyan
Verified answer
Task/26666597
---------------------
1)
x² - 49x +180 < 0 ; * * * x² - 49x +180 = (x - x₁)*(x - x₂) * * *
(x -4)(x -45) < 0 ;
методом координат:
+ - +
------------- (4) /////////////////// (45) -----------------
ответ : x ∈ (4 ; 45) .
-------------
2)
16x² - x ≥ 0 ;
16x(x -1/16) ≥
0 ;
+ - +
////////////////////// [0] -----------------[ 1/16 ] ///////////////////////
ответ: x
∈( -∞ ; 0] ∪ [ 1/16 ; ∞) .
-------------
3)
(2x -4)
/
(x+3) < 0⇔2(x -2)
/
(x+3) < 0 ⇔(x -2)
/
(x+3) < 0⇔ (x -2)*(x+3) < 0.
(x +3)*(x-2) < 0
.
+ - +
----------------- (-3)/////////////////////// (2) ----------------------
ответ: x
∈( - 3 ; 2 ) .
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Verified answer
Task/26666597---------------------
1)
x² - 49x +180 < 0 ; * * * x² - 49x +180 = (x - x₁)*(x - x₂) * * *
(x -4)(x -45) < 0 ;
методом координат:
+ - +
------------- (4) /////////////////// (45) -----------------
ответ : x ∈ (4 ; 45) .
-------------
2)
16x² - x ≥ 0 ;
16x(x -1/16) ≥ 0 ;
+ - +
////////////////////// [0] -----------------[ 1/16 ] ///////////////////////
ответ: x ∈( -∞ ; 0] ∪ [ 1/16 ; ∞) .
-------------
3)
(2x -4) / (x+3) < 0⇔2(x -2) / (x+3) < 0 ⇔(x -2) / (x+3) < 0⇔ (x -2)*(x+3) < 0.
(x +3)*(x-2) < 0.
+ - +
----------------- (-3)/////////////////////// (2) ----------------------
ответ: x ∈( - 3 ; 2 ) .