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