Task/27047191
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4.
y =(x+1)/6 +20/(x-1) - 4 =( (x+1)(x-1)+6*20 -4*6(x-1) ) /6(x-1) =
(x² -1 +120 -24x+24) / 6(x-1) = (x²- 24x+143)/6(x-1) =( (x-12)² -1 ) /6(x-1) =
(x -11)(x -13)/6(x-1) .
1)
y < 0 ⇔(x -11)(x -13) / (x-1) < 0 ⇔(x-1)(x -11)(x -13) < 0
" -" "+" "-" "+"
///////////////////// (1) ------------------(11) ///////////////////// (13) -----------
x ∈( -∞; 1) ∪ (11; 13).
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2) y ≥ 0⇔ (x -11)(x -13)/(x-1) ≥ 0 ⇒x ∈(1;11] ∪ [13 ; ∞).
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3) y = 0 ⇔ (x -11)(x -13)/(x-1)=0 ⇒x ∈{ 11; 13} . * * * 11 или 13 * * *
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5.При каких значениях a неравенство выполняется при любых значениях
x:
1)
(x-4)² > 3a²-60 +3a .
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3a²-60+3a < 0 ;
3(a²+a-20 ) < 0 ; <br>3(a +5)(a- 4) <0 ;<br>a∈(-5 ;4).
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2)
- x² - 6x +4a - 8 ≤ 0 ⇔ - (x+3)² +4a+ 1 ≤ 0 ⇔ (x+3)² ≥ 4a+ 1 .
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4a+ 1 ≤ 0 ;
a ≤ -1/4 иначе a ∈ (-∞ ; -0,25].